Christian Krattenthaler | Academic Influence

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Christian Krattenthaler

Mathematics

#2646

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#4051

Historical Rank

Combinatorics

#64

World Rank

#71

Historical Rank

Measure Theory

#2478

World Rank

#2979

Historical Rank

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Mathematics

Christian Krattenthaler's Degrees

PhD Mathematics University of Vienna

Why Is Christian Krattenthaler Influential?

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According to Wikipedia, Christian Friedrich Krattenthaler is an Austrian mathematician. He is a professor of discrete mathematics . From 2016 to 2020 he has been the Dean of the Faculty of Mathematics at the University of Vienna.

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Christian Krattenthaler's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

ADVANCED DETERMINANT CALCULUS (1999) (526)
Advanced Determinant Calculus: A Complement (2005) (282)
Permutations with Restricted Patterns and Dyck Paths (2000) (243)
Vicious walkers, friendly walkers and Young tableaux: II. With a wall (2000) (147)
Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes (2005) (144)
Superconformal indices of three-dimensional theories related by mirror symmetry (2011) (132)
Cylindric Partitions (1995) (106)
A new matrix inverse (1996) (91)
Lattice Path Enumeration (2015) (90)
Enumeration of Lozenge Tilings of Hexagons with a Central Triangular Hole (1999) (82)
The major counting of nonintersecting lattice paths and generating functions for tableaux (1995) (80)
Non-commutative Hopf algebra of formal diffeomorphisms (2004) (79)
Summations for basic hypergeometric series involving a q-analogue of the digamma function (1996) (77)
Generating functions for plane partitions of a given shape (1990) (67)
Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets (1998) (58)
Operator methods and Lagrange inversion: a unified approach to Lagrange formulas (1988) (57)
Identities for Classical Group Characters of Nearly Rectangular Shape (1998) (56)
Lattice Path Proofs for Determinantal Formulas for Symplectic and Orthogonal Characters (1997) (54)
Enumeration of Lozenge Tilings of Hexagons with Cut-Off Corners (2001) (53)
Another Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula (1998) (50)
Stanley decompositions and Hilbert depth in the Koszul complex (2009) (50)
Plane partitions in the work of Richard Stanley and his school (2015) (49)
Automatic generation of hypergeometric identities by the beta integral method (2003) (49)
On the integrality of the Taylor coefficients of mirror maps (2007) (48)
The Enumeration of Lattice Paths With Respect to Their Number of Turns (1997) (48)
Descending plane partitions and rhombus tilings of a hexagon with a triangular hole (2003) (41)
Symmetry Classes (1998) (39)
Regular sequences of symmetric polynomials (2008) (38)
THE THEORY OF HEAPS AND THE CARTIER–FOATA MONOID (38)
An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series (2003) (38)
Vicious Walkers, Friendly Walkers, and Young Tableaux. III. Between Two Walls (2002) (36)
A dual of MacMahon’s theorem on plane partitions (2012) (36)
Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted (1995) (36)
Plane partitions II: 5 1/2 symmetry classes (1998) (35)
The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, I (1997) (34)
Watermelon configurations with wall interaction: exact and asymptotic results (2005) (33)
Determinant Identities and a Generalization of the Number of Totally Symmetric Self-complementary Plane Partitions (1997) (32)
ad-nilpotent $\frak b$-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumeration (2000) (32)
On theq-log-concavity of Gaussian binomial coefficients (1989) (32)
A new multidimensional matrix inverse with applications to multiple q-series (1999) (31)
Some New Formulas for π (2003) (31)
Determinants of (generalised) Catalan numbers (2007) (30)
On the Number of Fully Packed Loop Configurations with a Fixed Associated Matching (2005) (29)
Enumeration of ad-Nilpotent b-Ideals for Simple Lie Algebras (2002) (28)
A NEW q-LAGRANGE FORMULA AND SOME APPLICATIONS (1984) (28)
Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions (2007) (28)
Some divisibility properties of binomial and q-binomial coefficients (2013) (28)
-nilpotent -ideals in () having a fixed class of nilpotence: combinatorics and enumeration (2002) (27)
The Interaction of a Gap with a Free Boundary in a Two Dimensional Dimer System (2009) (27)
The Number of Rhombus Tilings of a “Punctured” Hexagon and the Minor Summation Formula (1997) (27)
Asymptotic redundancies for universal quantum coding (1996) (27)
Some determinants of path generating functions (2009) (26)
A remarkable formula for counting nonintersecting lattice paths in a ladder with respect to turns (1999) (26)
The Hilbert Series of Pfaffian Rings (2001) (26)
How can we escape Thomae's relations? (2005) (25)
HYP and HYPQ Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively q-binomial sums and basic hypergeometric series (1993) (25)
The Number of Centered Lozenge Tilings of a Symmetric Hexagon (1997) (25)
On Lattice Path Counting by Major Index and Descents (1993) (25)
HYP and HYPQ (1995) (25)
The F-triangle of the Generalised Cluster Complex (2005) (24)
Evaluations of some determinants of matrices related to the Pascal triangle (2001) (22)
Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method (2016) (22)
Proof of two conjectures of Zuber on fully packed loop configurations (2003) (21)
ASYMPTOTICS FOR RANDOM WALKS IN ALCOVES OF AFFINE WEYL GROUPS (2003) (21)
Lattice Paths, Reeections, & Dimension-changing Bijections (1992) (21)
A Method for Determining the Mod-2k Behaviour of Recursive Sequences, with Applications to Subgroup Counting (2011) (19)
Schur function identities and the number of perfect matchings of holey Aztec rectangles (1997) (19)
ON q-ANALOGUES OF SOME SERIES FOR π AND π 2 (2019) (18)
Combinatorial Proof of the Log-Concavity of the Sequence of Matching Numbers (1996) (18)
A method for determining the mod-$p^k$ behaviour of recursive sequences (2013) (18)
An Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula (1998) (17)
Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps (2008) (17)
On multiplicities of points on Schubert varieties in Grassmannians. (2000) (17)
An Alternative Evaluation of the Andrews-Burge Determinant (1998) (17)
On the Problem of Electromagnetic-Field Quantization (2013) (17)
A determinant evaluation and some enumeration results for plane partitions (1990) (17)
ON LATTICE PATH COUNTING BY MAJOR AND DESCENTS (1990) (16)
On Multiplicities of Points on Schubert Varieties in Graßmannians II (2001) (16)
Enumeration of lattice paths and generating functions for skew plane partitions (1989) (16)
A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings (2008) (16)
Discrete analogues of Macdonald-Mehta integrals (2016) (16)
Heine transformations for a new kind of basic hypergeometric series in U ( n ) (1996) (15)
An entry of Ramanujan on hypergeometric series in his Notebooks (2003) (14)
Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams (2014) (12)
A Determinantal Formula for the Hilbert Series of One-sided Ladder Determinantal Rings (2001) (12)
A factorization theorem for lozenge tilings of a hexagon with triangular holes (2014) (12)
The M-triangle of generalised non-crossing partitions for the types E7 and E8 (2006) (12)
On conformal powers of the Dirac operator on Einstein manifolds (2014) (12)
Cyclic Sieving for Generalised Non-crossing Partitions Associated with Complex Reflection Groups of Exceptional Type (2009) (11)
Non-crossing two-rowed arrays and summations for Schur functions (1993) (11)
Counting pairs of nonintersecting lattice paths with respect to weighted turns (1996) (11)
COUNTING NONINTERSECTING LATTICE PATHS WITH TURNS (2000) (11)
On the non-quadraticity of values of the q-exponential function and related $q$-series (2008) (11)
Oscillating tableaux and nonintersecting lattice paths (1996) (11)
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van der Poorten (1998) (11)
A bijection between Proctor's and Sundaram's odd orthogonal tableaux (1996) (10)
The major index generating function of standard Young tableaux of shapes of the form "staircase minus rectangle" (2014) (10)
Generating functions for shifted plane partitions (1993) (10)
On Group Theoretical Aspects, Hypergeometric Transformations and Symmetries of Angular Momentum Coefficients (2004) (10)
Hilbert depth of powers of the maximal ideal (2010) (10)
Recent Progress in the Study of Representations of Integers as Sums of Squares (2004) (10)
On $q$-analogues of some series for $\pi $ and $\pi ^2$ (2018) (9)
ON “ A NOTE ON THE DISTRIBUTION OF THE THREE TYPES OF NODES IN UNIFORM BINARY TREES ” BY (1996) (9)
SOME q-ANALOGUES OF DETERMINANT IDENTITIES WHICH AROSE IN PLANE PARTITION ENUMERATION (1996) (9)
Graphical major indices. II. (1995) (9)
The Flagged Cauchy Determinant (2005) (9)
Motzkin numbers and related sequences modulo powers of 2 (2016) (7)
PROOF OF A SUMMATION FORMULA FOR AN Ãn BASIC HYPERGEOMETRIC SERIES CONJECTURED BY WARNAAR (2001) (7)
Bijections for Hook Pair Identities (1999) (7)
Euler Characteristic of the Truncated Order Complex of Generalized Noncrossing Partitions (2009) (7)
A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin (1995) (7)
On a linear form for Catalan's constant (2008) (7)
A new proof of the M-R-R conjecture-including a generalization (1999) (7)
Rectangular Scott-type Permanents (2000) (6)
Parity patterns associated with lifts of Hecke groups (2008) (6)
Supercongruences satisfied by coefficients of 2F1 hypergeometric series (2009) (6)
HYPERGEOMETRY INSPIRED BY IRRATIONALITY QUESTIONS (2018) (6)
Counting tableaux with row and column bounds (1995) (6)
The rank enumeration of certain parabolic non-crossing partitions (2019) (6)
Q-generalization of a Ballot Problem (1994) (6)
Evaluation of binomial double sums involving absolute values (2016) (5)
ANALYTIC PROPERTIES OF MIRROR MAPS (2011) (5)
DECOMPOSABLE FUNCTORS AND THE EXPONENTIAL PRINCIPLE, II (2009) (5)
Some determinants of path generating functions, II (2009) (5)
2-adic valuations of certain ratios of products of factorials and applications (2005) (5)
Lattice Path Combinatorics (2006) (4)
The poset of bipartitions (2009) (4)
Truncated versions of Dwork's lemma for exponentials of power series and $p$-divisibility of arithmetic functiens (2014) (4)
A determinant of generalized Fibonacci numbers (2012) (4)
Bounded Dyck paths, bounded alternating sequences, orthogonal polynomials, and reciprocity (2020) (4)
On the integrality of Taylor coefficients of mirror maps in several variables (2008) (4)
On bideterminantal formulas for characters of classical groups (1995) (4)
Some composition determinants (2005) (4)
Counting triangulations of some classes of subdivided convex polygons (2016) (4)
Q-Analogue of a Two Variable Inverse Pair of Series with Applications to Basic Double Hypergeometric Series (1989) (3)
Asymptotic analysis of a Selberg-type integral via hypergeometrics (2010) (3)
Equations in finite semigroups: explicit enumeration and asymptotics of solution numbers (2003) (3)
Best polynomial approximation on the triangle (2017) (3)
Hankel determinants of linear combinations of moments of orthogonal polynomials (2020) (3)
Lattice Path Combinatorics and Applications (2019) (3)
Chromatic Statistics for Triangulations and Fuß-Catalan Complexes (2011) (3)
Plane partitions II: $5\frac{1}{2}$ symmetry classes (2000) (3)
A Riccati differential equation and free subgroup numbers for lifts of PSL2(Z)PSL2(Z) modulo prime powers (2013) (3)
On a hypergeometric identity of Gelfand, Graev and Retakh (2003) (3)
Periodicity of free subgroup numbers modulo prime powers (2014) (3)
Multistability and Multi 2π-KINKS in the Frenkel-Kontorova Model:. AN Application to Arrays of Josephson Junctions (2007) (2)
The Determinant of an Elliptic Sylvesteresque Matrix (2018) (2)
A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which Contain a Fixed Rhombus (2001) (2)
A non-automatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration (2000) (2)
Computation of the $a$-invariant of ladder determinantal rings (2015) (2)
Proof of two multivariate $q$-binomial sums arising in Gromov-Witten theory (2021) (2)
Lucas congruences for the Ap\'ery numbers modulo $p^2$ (2020) (2)
Trace identities from identities for determinants (2004) (2)
Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold (2019) (2)
On (shape-)Wilf-equivalence for words (2018) (2)
Some new formulas for $\pi$ (2001) (2)
Generalised Ap\'ery numbers modulo $9$ (2014) (2)
A determinant identity for moments of orthogonal polynomials that implies Uvarov's formula for the orthogonal polynomials of rationally related densities (2021) (1)
A Riccati differential equation and free subgroup numbers for lifts of $\PSL_2(\Z)$ modulo powers of primes (2012) (1)
On the Problem of Electromagnetic-Field Quantization (2013) (1)
Normalising graphs of groups (2016) (1)
The Research Training Network “Algebraic Combinatorics in Europe” (2005) (1)
Hankel determinants of linear combinations of moments of orthogonal polynomials, II (2021) (1)
Mathematik und Musik? (2014) (1)
Free subgroup numbers modulo prime powers: The non-periodic case (2016) (1)
Counting triangulations of balanced subdivisions of convex polygons (2016) (1)
Enumeration of symmetric centered rhombus tilings of a hexagon (2013) (1)
Summation formulas for GJMS-operators and Q-curvatures on the Möbius sphere (2009) (1)
2 N ov 2 00 5 SOME COMPOSITION DETERMINANTS (2005) (0)
Discrete Random Walks, DRW'03, Paris, France, September 1-5, 2003 (2003) (0)
MULTISTABILITY AND MULTI 2π-KINKS IN THE FRENKEL–KONTOROVA MODEL: AN APPLICATION TO ARRAYS OF JOSEPHSON JUNCTIONS (2007) (0)
An Eigenvalue Problem for the Associated Askey–Wilson Polynomials (2012) (0)
The Hilbert Series of PfaÆan (2007) (0)
Two Combinatorial Identities (Ma Xin-Bong and Wang Tian-Ming) (1996) (0)
A note on higher-dimensional magic matrices (2011) (0)
Preface (2017) (0)
Analytic proof of the partition identity $A_{5,3,3}(n) = B^0_{5,3,3}(n)$ (2004) (0)
Proof of a summation formula for an $\tilde A_n$ basic hypergeometric series conjectured by Warnaar (2002) (0)
Buchbesprechunge@@@Book reviews (1979) (0)
Domino tilings of generalized Aztec triangles (2023) (0)
O ct 2 00 5 SOME COMPOSITION DETERMINANTS (2005) (0)
Summation formulas for GJMS-operators and Q-curvartures (2011) (0)
Chromatic statistics for Catalan and Fu{\ss}-Catalan numbers (2011) (0)
Normalising graphs of groups (2016) (0)
Analytic proof of the partition identity A5,3,3(n)=B5,3,30(n) (2008) (0)
Am DECOMPOSABLE FUNCTORS AND THE EXPONENTIAL PRINCIPLE , II (2010) (0)
The congruence properties of Romik's sequence of Taylor.coefficients of Jacobi's theta function $\theta_3$ (2023) (0)
ENUMERATION OF RHOMBUS TILINGS OF A HEXAGON WHICH CONTAIN A FIXED RHOMBUS ON ITS SYMMETRY AXIS (EXTENDED ABSTRACT) (1997) (0)
Enumerative Combinatorics (2019) (0)
Preface (2020) (0)
LATTICE PATH (2010) (0)
On conformal powers of the Dirac operator on Einstein manifolds (2015) (0)
Thomas Muir: ‘Lad O’ Pairts’. The Life and Work of Sir Thomas Muir (1844–1934), Mathematician and Cape Colonial Educationist by Peter Elliott (2022) (0)
Identities for vacillating tableaux via growth diagrams (2023) (0)
Infinite Product Formulae for Generating Functions for Sequences of Squares (2019) (0)
The Hilbert Series of PfaÆan Rings ? (2007) (0)
Discrete Random Walks: Theory and applications in combinatorics, computational biology, computer science, probability theory, and statistical physics. (2003) (0)
Model Theory and Complex Analytic Geometry (2004) (0)
Spiral determinants (2017) (0)
Enumeration of ad-nilpotent $\frak b$-ideals for simple Lie algebras (2000) (0)
A ] 7 J un 2 00 4 Non-commutative Hopf algebra of formal diffeomorphisms (2008) (0)
N T ] 1 0 O ct 2 00 2 SOME NEW FORMULAS FOR π (2021) (0)
One-variable q-analogues for Abhyankar's inversion formula (1989) (0)
An asymptotic approach to Borwein-type sign pattern theorems (2022) (0)
Affine Gordon-Bender-Knuth identities for cylindric Schur functions (2023) (0)
Short biography of Shmuel Friedland for his special LAA volume (2009) (0)
Discrete Random Walks 2003: Introduction and Acknowledgements (2006) (0)
Book Reviews (2002) (0)
ANALYTIC PROOF OF THE PARTITION IDENTITY A5,3,3(n) = B 0 5,3,3 (n) PADMAVATHAMMA, CHANDRASHEKARA B.M., RAGHAVENDRA R., AND (2004) (0)
DESCRIPTION OF THE STRASBOURG GROUP A. The group itself. In the field of Algebraic Combinatorics there are six people in Strasbourg enrolled in the EEC Human Capital and Mobility Programme, namely (2000) (0)
MOMENTS OF q-JACOBI POLYNOMIALS AND q-ZETA VALUES (2020) (0)
A joint central limit theorem for the sum-of-digits function, and asymptotic divisibility of Catalan-like sequences (2018) (0)
Congruences modulo powers of $2$ for the number of unique path partitions (2016) (0)
Mathematics AND Music? Personal Views on a Difficult Relationship (2017) (0)

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What Schools Are Affiliated With Christian Krattenthaler?

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University of Vienna

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