# Péter Frankl

Hungarian mathematician and street performer in Japan

## Péter Frankl's AcademicInfluence.com Rankings

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Mathematics

## Péter Frankl's Degrees

- PhD Mathematics Eötvös Loránd University
- Masters Mathematics Eötvös Loránd University

## Why Is Péter Frankl Influential?

(Suggest an Edit or Addition)According to Wikipedia, Péter Frankl is a mathematician, street performer, columnist and educator, active in Japan. Frankl studied mathematics at Eötvös Loránd University in Budapest and submitted his PhD thesis while still an undergraduate. He holds a PhD degree from the University Paris Diderot as well. He has lived in Japan since 1988, where he is a well-known personality and often appears in the media. He keeps travelling around Japan performing . Frankl won a gold medal at the International Mathematical Olympiad in 1971. He has seven joint papers with Paul Erdős, and eleven joint papers with Ronald Graham. His research is in combinatorics, especially in extremal combinatorics. He is the author of the union-closed sets conjecture.

## Péter Frankl's Published Works

### Published Works

- Intersection theorems with geometric consequences (1981) (532)
- Families of finite sets in which no set is covered by the union ofr others (1985) (450)
- The Johnson-Lindenstrauss lemma and the sphericity of some graphs (1987) (346)
- Complexity classes in communication complexity theory (1986) (320)
- The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent (1986) (291)
- Some intersection theorems for ordered sets and graphs (1986) (279)
- On the Maximum Number of Permutations with Given Maximal or Minimal Distance (1977) (259)
- An Extremal Problem for two Families of Sets (1982) (197)
- Extremal problems on set systems (2002) (187)
- The Erdös-Ko-Rado theorem for vector spaces (1986) (185)
- Linear Algebra Methods in Combinatorics I (1988) (185)
- Erdös–Ko–Rado Theorem—22 Years Later (1983) (172)
- Near Perfect Coverings in Graphs and Hypergraphs (1985) (157)
- Families of Finite Sets in Which No Set Is Covered by the Union of Two Others (1982) (155)
- Hypergraphs do not jump (1984) (153)
- A new generalization of the Erdős-Ko-Rado theorem (1983) (152)
- Cops and robbers in graphs with large girth and Cayley graphs (1987) (147)
- Improved bounds for Erdős' Matching Conjecture (2013) (128)
- On intersecting families of finite sets (1978) (121)
- Large triangle-free subgraphs in graphs withoutK4 (1986) (116)
- Large matchings in uniform hypergraphs and the conjectures of Erdős and Samuels (2011) (115)
- Extremal problems whose solutions are the blowups of the small witt-designs (1989) (112)
- Extremal set systems (1996) (110)
- Geometrical realization of set systems and probabilistic communication complexity (1985) (108)
- On the Trace of Finite Sets (1983) (105)
- On Sperner Families Satisfying an Additional Condition (1976) (99)
- Exact solution of some Turán-type problems (1987) (98)
- Forbidding Just One Intersection (1985) (96)
- The Uniformity Lemma for hypergraphs (1992) (94)
- An exact result for 3-graphs (1984) (90)
- Complexity classes in communication complexity theory (preliminary version) (1986) (89)
- INTERSECTION PROPERTIES OF SYSTEMS OF FINITE SETS (1978) (87)
- Shadows of colored complexes. (1988) (86)
- A Hilton-Milner Theorem for Vector Spaces (2010) (84)
- A new short proof for the Kruskal-Katona theorem (1984) (78)
- Erdös-Ko-Rado theorem with conditions on the maximal degree (1987) (77)
- On the maximum number of edges in a hypergraph with given matching number (2012) (72)
- The Erdős–Ko–Rado Theorem for Integer Sequences (1999) (71)
- The chromatic number of kneser hypergraphs (1986) (68)
- A short proof for a theorem of Harper about Hamming-spheres (1981) (67)
- On subsets of abelian groups with no 3-term arithmetic progression (1987) (65)
- A partition property of simplices in Euclidean space (1990) (64)
- Isomorphisms of Cayley graphs. II (1979) (61)
- Quantitative theorems for regular systems of equations (1988) (60)
- The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem (1987) (59)
- Some Best Possible Inequalities Concerning Cross-Intersecting Families (1992) (59)
- Invitation to intersection problems for finite sets (2016) (58)
- Intersection theorems and mod p rank of inclusion matrices (1990) (58)
- Non-trivial intersecting families (1986) (55)
- Some geometric applications of the beta distribution (1990) (53)
- Union-free Hypergraphs and Probability Theory (1984) (50)
- The number of submatrices of a given type in a Hadamard matrix and related results (1988) (50)
- On families of finite sets no two of which intersect in a singleton (1977) (49)
- Extremal problems concerning Kneser graphs (1986) (45)
- On the Number of Sets in a Null t-Design (1983) (45)
- On the Maximum Number of Edges in a Triple System Not Containing a Disjoint Family of a Given Size (2012) (44)
- The Erdős Matching Conjecture and concentration inequalities (2022) (44)
- Solution of the Littlewood-Offord problem in high dimensions (1988) (43)
- Beyond the Erdös-Ko-Rado theorem (1991) (42)
- On Matchings in Hypergraphs (2012) (42)
- On a pursuit game on cayley graphs (1987) (40)
- Improved bounds for Erd ˝ os' Matching Conjecture (2013) (39)
- A note on the jumping constant conjecture of Erdös (2007) (39)
- Covers in Uniform Intersecting Families and a Counterexample to a Conjecture of Lovász (1996) (37)
- All triangles are Ramsey (1986) (37)
- On disjointly representable sets (1984) (37)
- A new short proof of the EKR theorem (2011) (36)
- Finite projective spaces and intersecting hypergraphs (1986) (35)
- Extremal hypergraph problems and convex hulls (1985) (35)
- Codes with given distances (1987) (33)
- Good coverings of Hamming spaces with spheres (1985) (33)
- Intersecting sperner families and their convex hulls (1984) (32)
- An Erdős-Ko-Rado theorem for cross t-intersecting families (2013) (32)
- Asymptotic solution of a turán-type problem (1990) (32)
- Weighted multiply intersecting families (2003) (31)
- Proof of the Erdős matching conjecture in a new range (2017) (31)
- On the size of graphs with complete-factors (1985) (31)
- Two problems on matchings in set families - In the footsteps of Erdős and Kleitman (2016) (30)
- Some Ramsey-Turán type results for hypergraphs (1988) (29)
- Orthogonal vectors in then-dimensional cube and codes with missing distances (1986) (29)
- Lower bounds for Turán's problem (1985) (28)
- Minimum Shadows in Uniform Hypergraphs and a Generalization of the Takagi Function (1995) (27)
- An Erdos-Ko-Rado Theorem for Direct Products (1996) (27)
- Multiply-intersecting families (1990) (27)
- Erdős-Ko-Rado theorem for {0, ±1}-vectors (2018) (27)
- The Erdös-Ko-Rado Theorem for Integer Sequences (1980) (26)
- The Sperner Capacity of Linear and Nonlinear Codes for the Cyclic Triangle (1993) (25)
- Intersecting Families of Finite Sets and Fixed-point-Free 2-Elements (1989) (24)
- FAMILIES OF FINITE SETS WITH MISSING INTERSECTIONS (1984) (24)
- Extremal k-edge-hamiltonian Hypergraphs (2008) (24)
- Set Systems with Restricted Intersections modulo Prime Powers (2001) (23)
- On r-Cross Intersecting Families of Sets (2011) (23)
- Intersection Theorems for Vector Spaces (1985) (23)
- On Hypergraphs without Two Edges Intersecting in a Given Number of Vertices (1984) (23)
- Every large set of equidistant (0, +1, −1)-vectors forms a sunflower (1981) (22)
- Shadows and shifting (1991) (22)
- Induced restricted Ramsey theorems for spaces (1987) (22)
- On Set Intersections (1980) (21)
- On the Minimum Number of Disjoint Pairs in a Family of Finite Sets (1977) (20)
- Families of finite sets satisfying an intersection condition (1976) (20)
- Sharp Sets of Permutations (1987) (20)
- Extremal Problems and Coverings of the Space (1980) (20)
- What must be contained in every oriented k-uniform hypergraph (1986) (20)
- A generalization of Sperner's theorem (1981) (19)
- All rationals occur as exponents (1986) (19)
- On functions of strengtht (1983) (19)
- Bounding one-way differences (1987) (18)
- Traces of antichains (1989) (18)
- Families with no s pairwise disjoint sets (2016) (18)
- Counting Intersecting and Pairs of Cross-Intersecting Families (2017) (17)
- Colored packing of sets (1987) (17)
- Families of finite sets satisfying a union condition (1979) (17)
- A size-sensitive inequality for cross-intersecting families (2016) (16)
- On the chromatic number of the general Kneser-graph (1985) (16)
- On a Problem of Chvátal and Erdös on Hypergraphs Containing No Generalized Simplex (1981) (16)
- The maximum number of disjoint pairs in a family of subsets (1985) (15)
- A lower bound on the size of a complex generated by an antichain (1989) (15)
- On the number of maximal dependencies in a data base relation of fixed order (1980) (15)
- Simple juntas for shifted families (2019) (15)
- Extremal Problems for Finite Sets (2018) (15)
- Open-interval graphs versus closed-interval graphs (1987) (15)
- Probabilities for intersecting systems and random subsets of finite sets (1986) (15)
- A Finite Set Intersection Theorem (1981) (15)
- Union-Free Families of Sets and Equations over Fields (1986) (15)
- Families of sets with no matchings of sizes 3 and 4 (2017) (15)
- Weighted 3-Wise 2-Intersecting Families (2002) (15)
- Bounds on the maximum number of vectors with given scalar products (1985) (14)
- On a Conjecture of Chvátal on m -Intersecting Hypergraphs (1977) (14)
- Random walks and multiply intersecting families (2005) (14)
- BPP and the polynomial time hierarchy in communication complexity (1986) (14)
- Uniform Intersecting Families with Covering Number Four (1995) (14)
- Families of finite sets with prescribed cardinalities for pairwise intersections (1980) (13)
- Maximal independent sets in bipartite graphs obtained from Boolean lattices (2011) (13)
- Uniform s-Cross-Intersecting Families (2016) (13)
- Extremal problems in finite geometry (1994) (13)
- On tilings of the binary vector space (1991) (13)
- Embedding the n-cube in Lower Dimensions (1986) (12)
- Some Inequalities Concerning Cross-Intersecting Families (1998) (12)
- Generalizations of theorems of Katona and Milner (1976) (12)
- On the contact dimensions of graphs (1988) (12)
- A helly type theorem for hypersurfaces (1987) (12)
- The maximum number of edges in a 3-graph not containing a given star (1987) (12)
- A degree version of the Hilton-Milner theorem (2017) (12)
- An extremal problem for 3-graphs (1978) (12)
- The Erd\H{o}s Matching Conjecture and concentration inequalities. (2018) (12)
- A new extremal property of Steiner triple-systems (1984) (12)
- Binary codes and quasi-symmetric designs (1990) (12)
- The number of sub-matrics of a given type in a Hadamard matrix and related results (1987) (11)
- Two problems of P. Erdős on matchings in set families (2016) (11)
- Linear Dependencies among Subsets of a Finite Set (1983) (11)
- An Erdös-Ko-Rado Theorem for Integer Sequences of Given Rank (1986) (11)
- Constructing Finite Sets With Given Intersections (1983) (11)
- On the number of nonnegative sums (2013) (11)
- New inequalities for families without k pairwise disjoint members (2018) (11)
- An intersection problem for finite sets (1977) (10)
- Families of vectors without antipodal pairs (2017) (10)
- Exponents of Uniform L-Systems (1996) (10)
- The Proof of a Conjecture of G. O. H. Katona (1975) (10)
- On the vector space of 0-configurations (1982) (10)
- Regularity conditions and intersecting hypergraphs (1981) (10)
- Sharpening the LYM inequality (1992) (10)
- Simplices with Given 2-Face Areas (1990) (10)
- On Subsets with Cardinalities of Intersections Divisible by a Fixed Integer (1983) (10)
- Weighted Non-Trivial Multiply Intersecting Families (2006) (10)
- A simple proof of the Hilton–Milner theorem (2019) (9)
- Partition‐free families of sets (2019) (8)
- Sets of Vectors with Many Orthogonal Pairs (1992) (8)
- Helly-type Theorems for Varieties (1989) (8)
- The Radon transform on Abelian Groups (1987) (8)
- An extremal set theoretical characterization of some steiner systems (1983) (8)
- Maximal independent sets in the covering graph of the cube (2013) (8)
- Inequalities for Subsets of a Set and KLYM Posets (1983) (8)
- Families of finite sets with three intersections (1984) (8)
- Maximum degree and diversity in intersecting hypergraphs (2020) (8)
- A note on Huang-Zhao theorem on intersecting families with large minimum degree (2017) (8)
- Matroids, Algebraic and Non Algebraic (1988) (7)
- Sets of finite sets satisfying union conditions (1982) (7)
- Local Turán property for k-graphs (1981) (7)
- Algebraic, extremal and metric combinatorics, 1986 (1988) (7)
- Some exact results for multiply intersecting families (2019) (7)
- Canonical Antichains on the Circle and Applications (1990) (7)
- Some best possible bounds concerning the traces of finite sets (1994) (7)
- Families in Which Disjoint Sets Have Large Union (1989) (7)
- Polytopes Determined by Hypergraph Classes (1985) (7)
- A note on supersaturated set systems (2016) (7)
- On squashed design (1986) (7)
- How (Not) to Cut Your Cheese (2021) (6)
- If the intersection of any r sets has a size ̸= r − 1 (1979) (6)
- Sharp results concerning disjoint cross-intersecting families (2019) (6)
- Intersection theorems for {0, ±1}-vectors and s-cross-intersecting families (2016) (6)
- Some recent results on Ramsey-type numbers (2013) (6)
- A near-exponential improvement of a bound of Erdős and Lovász on maximal intersecting families (2019) (6)
- A General Intersection Theorem For Finite Sets (1980) (6)
- Hamiltonian Cubic Graphs and Centralizers of Involutions (1979) (5)
- Strong ramsey properties of simplices (2004) (5)
- On the number of elements which are not n-th powers in finite groups (1989) (5)
- On the maximum number of distinct intersections in an intersecting family (2021) (5)
- A sharpening of Fisher's inequality (1991) (5)
- A Stability Result for Families with Fixed Diameter (2017) (5)
- Intersections and distinct intersections in cross-intersecting families (2022) (5)
- An extremal problem on Kr-free graphs (1988) (5)
- Improved Upper Bounds Concerning the Erdős-Ko-Rado Theorem (1992) (5)
- Intersection problems in the q-ary cube (2016) (5)
- Uniform eventown problems (2016) (4)
- The Katona theorem for vector spaces (2013) (4)
- Cells in the box and a hyperplane (2020) (4)
- Iterated combinatorial density theorems (1990) (4)
- The game of n-times nim (2003) (4)
- Old and new applications of Katona's circle (2020) (4)
- Erd\H os-Ko-Rado theorem for $\{0,\pm 1\}$-vectors (2015) (4)
- Intersection Theorems for Finite Sets and Geometric Applications (2010) (4)
- Intersection and Containment Problems Without Size Restrictions (1988) (4)
- Resilient Hypergraphs with Fixed Matching Number (2018) (4)
- Families with no matchings of size s (2017) (4)
- Covering Graphs by Equivalence Relations (1982) (4)
- A Product Version of the Hilton-Milner Theorem (2022) (4)
- Families of finite sets containing nok disjoint sets and their union (1977) (4)
- The Maximum Size of 3-Wise Intersecting and 3-Wise Union Families (2006) (4)
- Analogues of Katona's and Milner's theorems for two families (2020) (4)
- Best possible bounds on the number of distinct differences in intersecting families (2021) (4)
- A stability result for the Katona theorem (2017) (4)
- On Generalized Perfect Codes and Steiner Systems (1983) (4)
- Turán graphs with bounded matching number (2022) (3)
- Partition-free families of sets (2017) (3)
- Weight functions on the Kneser graph and the solution of an intersection problem of Sali (1993) (3)
- On the maximum of the sum of the sizes of non-trivial cross-intersecting families (2022) (3)
- Infinite quasigroups with given regular automorphism groups (1978) (3)
- Erdős-Ko-Rado Theorem for a Restricted Universe (2020) (3)
- Multiply union families in Nn (2016) (3)
- Intersection Theorems for Triangles (2020) (3)
- Uniform Intersecting Families with Covering Number Restrictions (1998) (3)
- Sections of Varieties Over Finite Fields as Large Intersectionc Families (1985) (3)
- EXTREMAL PROBLEMS ON SET SYSTEMSPETER FRANKL AND VOJT (2002) (3)
- Injection geometries (1984) (3)
- Borsuk and Ramsey type questions in Euclidean space (2017) (3)
- Density results for uniform families (1994) (3)
- Graphs without rainbow triangles (2022) (3)
- A Sperner-type theorem for families of finite sets (1978) (3)
- Beyond the Erdős Matching Conjecture (2021) (3)
- On Kruskal's cascades and counting containments in a set of subsets (1983) (3)
- On t-distance sets of (0, ±1)-vectors (1983) (3)
- Reflecting a triangle in the plane (1993) (3)
- Incompatible Intersection Properties (2018) (3)
- On the number of distinct differences in an intersecting family (2021) (3)
- Intersection theorems for (-1, 0, 1)-vectors (2020) (2)
- On non-trivial families without a perfect matching (2020) (2)
- Uniform intersecting families with large covering number (2021) (2)
- How to build a barricade (1984) (2)
- On strengthenings of the intersecting shadow theorem (2021) (2)
- A structural result for 3-graphs (2017) (2)
- On cross-intersecting families (1992) (2)
- Analogues of Milner's Theorem for families without long chains and of vector spaces (2021) (2)
- An improved universal bound for t-intersecting families (2020) (2)
- DISJOINT r-TUPLES IN AN r-GRAPH WITH GIVEN MAXIMUM DEGREE (1983) (2)
- Two-colorings with many monochromatic cliques in both colors (2013) (2)
- Some results around the Erdős Matching Conjecture (2019) (2)
- Minimum degree and diversity in intersecting antichains (2020) (2)
- Intersection theorems in permutation groups (1988) (2)
- A short proof of Erdős’ conjecture for triple systems (2016) (2)
- Maximal degrees in subgraphs of Kneser graphs (2020) (2)
- On families of sets without k pairwise disjoint members (2017) (2)
- Exchange Properties of Finite Set-Systems (2021) (2)
- On commutator subgroups (1976) (2)
- A Variant of the VC-dimension with Applications to Depth-3 Circuits (2021) (2)
- On local Turán problems (2021) (2)
- Decomposition of a Cube into Nearly Equal Smaller Cubes (2015) (2)
- An exact result for $$(0, \pm \, 1)$$(0,±1)-vectors (2018) (1)
- On the Distribution of Monochromatic Configurations (1989) (1)
- On the sum of sizes of overlapping families (2021) (1)
- On the Minimum Number of Sets Comparable with Some Members of a Set of Finite Sets (1977) (1)
- The convex hull of antichains in posets (1992) (1)
- A Product Version of the Hilton-Milner-Frankl Theorem (2022) (1)
- Pseudo sunflowers (2022) (1)
- Almost intersecting families (2020) (1)
- A Note on Universal and Canonically Coloured Sequences (2009) (1)
- Beyond the Erd\H{o}s Matching Conjecture (2019) (1)
- On Cliques and Partitions in Hamming Spaces (1983) (1)
- Linear independence, a unifying approach to shadow theorems (2016) (1)
- Research Problems Graphs and Combinatorics (1985) (1)
- On the arithmetic mean of the size of cross-union families (2021) (1)
- On Large Vector Systems with Equal Scalar Products (1981) (1)
- Correction to the article Intersection theorems for (−1,0,1)-vectors and s-cross-intersecting families (2019) (1)
- On Well-Connected Sets of Strings (2021) (1)
- On Non-Empty Cross-Intersecting Families (2020) (1)
- A probabilistic proof for the lym-inequality (1983) (1)
- Elementary Problems: E1243, E2440, E2652, E2665-E2670 (1977) (1)
- Improved bounds on exact stability results of the Erd\H{o}s-Ko-Rado theorem (2022) (1)
- A short proof for an extension of the Erdős-Ko-Rado Theorem (2015) (1)
- Improved bounds on the maximum diversity of intersecting families (2023) (0)
- Resilient Hypergraphs with Fixed Matching Number (2017) (0)
- On the maximum number of edges in a hypergraph whose linegraph contains no cycle (1980) (0)
- Diversity (2020) (0)
- Proof of the Erdős matching conjecture in a new range (2017) (0)
- Four-vertex traces of finite sets (2023) (0)
- ON TILINGS OF THE BINARY VECTOR SPACE G. COHEN and P. FRANKL (2002) (0)
- Algebraic, Extremal and Metric Combinatorics, 1986: Introduction (1988) (0)
- On the problem of symmetrical flow past a given symmetrical profile with subsonic velocity at infinity and local supersonic velocities (1959) (0)
- An exact result for ( 0 , ± 1 ) -vectors (2018) (0)
- CPC volume 4 issue 4 Cover and Front matter (1995) (0)
- Short Proof of Erd\H os Conjecture for Triple Systems (2016) (0)
- Piercing the chessboard (2021) (0)
- On local Tur\'an problems (2020) (0)
- CPC volume 4 issue 1 Cover and Front matter (1995) (0)
- Intersecting families with sunflower shadows (2022) (0)
- List of my favorite publications (2014) (0)
- On the size of shadow-added intersecting families (2021) (0)
- Perfect matchings in down-sets (2022) (0)
- On the arithmetic mean of the size of cross-union families (2021) (0)
- MULTIPLY UNION FAMILIES IN N (2015) (0)
- On the domination number of a graph defined by containment (2019) (0)
- Extremal set theory for the binomial norm (2019) (0)
- CPC volume 3 issue 3 Cover and Front matter (1994) (0)
- Multiply union families in $\mathbb{N}^n$ (2015) (0)
- Non-trivial r-wise intersecting families (2023) (0)
- A note on the universal and canonically colored sequences (2009) (0)
- CPC volume 2 issue 4 Cover and Front matter (1993) (0)
- Constructive Ramsey Bounds and Intersection Theorems for Sets (1990) (0)
- A short proof of Erdős’ conjecture for triple systems (2017) (0)
- Maximal independent sets in bipartite graphs obtained (2011) (0)
- CPC volume 4 issue 2 Cover and Front matter (1995) (0)
- CPC volume 2 issue 3 Cover and Front matter (1993) (0)
- String graphs , graph drawing , computing with curves on surfaces (2004) (0)
- $\{0,\pm1\}$-vectors and $s$-cross-intersecting families (2016) (0)
- On the section of a convex polyhedron (1995) (0)
- TR-2009-029 A theorem on incidence matrices and quasirandom hypergraphs (2009) (0)
- CPC volume 1 issue 2 Cover and Front matter (1992) (0)
- CPC volume 1 issue 3 Cover and Front matter (1992) (0)
- Shattered matchings in intersecting hypergraphs (2020) (0)
- CPC volume 2 issue 1 Cover and Front matter (1993) (0)
- Proof of the Erd\H{o}s Matching Conjecture in a New Range (2018) (0)
- CPC volume 4 issue 3 Cover and Front matter (1995) (0)
- Improved bounds concerning the maximum degree of intersecting hypergraphs (2022) (0)
- Sets of Graphs Colourings (1982) (0)
- On the size of the product of overlapping families (2022) (0)
- On Functions of Strenth t (1983) (0)
- CPC volume 3 issue 4 Cover and Front matter (1994) (0)
- ON SUPERSATURATED SET SYSTEMS 1 (2014) (0)
- CPC volume 3 issue 1 Cover and Front matter (1994) (0)
- C O ] 1 3 Ju l 2 01 8 A stability theorem on cube tessellations (2018) (0)
- Best possible bounds concerning the set-wise union of families (2018) (0)
- Families of finite sets satisfying intersection restrictions (2020) (0)
- Extremal results for graphs avoiding a rainbow subgraph (2022) (0)
- A stability theorem on cube tessellations (2018) (0)
- On the maximum number of edges in hypergraphs with fixed matching and clique number (2020) (0)
- Minimum degree and diversity in intersecting antichains (2020) (0)
- On asymptotic local Tur\'an problems (2023) (0)
- Best possible bounds on the double-diversity of intersecting hypergraphs (2022) (0)
- CPC volume 2 issue 2 Cover and Front matter (1993) (0)
- An intersection problem for codes (1990) (0)
- Mixed matchings in graphs (2020) (0)

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