Proceedings of the London Mathematical Society, ISSN 0024-6115, 11/2018, Volume 117, Issue 5, pp. 1077 - 1100

We prove a conjecture of Naito–Sagaki about a branching rule for the restriction of irreducible representations of sl(2n,C) to sp(2n,C). The conjecture is in...

05E05 | 20G05 (primary) | 05E10 (secondary) | MATHEMATICS | LITTLEWOOD-RICHARDSON RULE

05E05 | 20G05 (primary) | 05E10 (secondary) | MATHEMATICS | LITTLEWOOD-RICHARDSON RULE

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 6/2019, Volume 174, Issue 1, pp. 133 - 176

We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a...

Statistics for Business, Management, Economics, Finance, Insurance | beta $$ β -ensemble | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Quantitative Finance | Random matrices | Secondary 20C30 | Operations Research/Decision Theory | Jack polynomials | Jack characters | Primary 05E05 | 60K35 | Random Young diagrams | beta $$β-ensemble | beta-ensemble | STATISTICS & PROBABILITY | CHARACTERS | Variation | Deformation

Statistics for Business, Management, Economics, Finance, Insurance | beta $$ β -ensemble | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Quantitative Finance | Random matrices | Secondary 20C30 | Operations Research/Decision Theory | Jack polynomials | Jack characters | Primary 05E05 | 60K35 | Random Young diagrams | beta $$β-ensemble | beta-ensemble | STATISTICS & PROBABILITY | CHARACTERS | Variation | Deformation

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 04/2016, Volume 93, Issue 2, pp. 301 - 318

We prove combinatorial rules that give the minimal and maximal partitions labelling the irreducible constituents of a family of characters for the symmetric...

MATHEMATICS | ALGEBRA SYSTEM | Mathematics - Representation Theory

MATHEMATICS | ALGEBRA SYSTEM | Mathematics - Representation Theory

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 8/2018, Volume 289, Issue 3, pp. 837 - 857

In 1936, Margarete C. Wolf showed that the ring of symmetric free polynomials in two or more variables is isomorphic to the ring of free polynomials in...

Secondary 05E05 | 13A50 | Free analysis | Symmetric functions in noncommuting variables | Noncommutative invariant theory | Mathematics, general | 47A56 | Mathematics | Invariant theory | 17A50 | 47A63 | Primary 46L52 | MATHEMATICS | INVARIANTS | HOLOMORPHIC-FUNCTIONS | NONCOMMUTING VARIABLES | OPERATORS

Secondary 05E05 | 13A50 | Free analysis | Symmetric functions in noncommuting variables | Noncommutative invariant theory | Mathematics, general | 47A56 | Mathematics | Invariant theory | 17A50 | 47A63 | Primary 46L52 | MATHEMATICS | INVARIANTS | HOLOMORPHIC-FUNCTIONS | NONCOMMUTING VARIABLES | OPERATORS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2018, Volume 290, Issue 1, pp. 445 - 467

In this paper we prove that the counting polynomials of certain torus orbits in products of partial flag varieties coincides with the Kac polynomials of...

05E05 | 05C31 | Mathematics, general | Mathematics | Secondary 14M15 | Primary 16G20 | MATHEMATICS | ARITHMETIC HARMONIC-ANALYSIS | CHARACTER | INVARIANT

05E05 | 05C31 | Mathematics, general | Mathematics | Secondary 14M15 | Primary 16G20 | MATHEMATICS | ARITHMETIC HARMONIC-ANALYSIS | CHARACTER | INVARIANT

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 07/2019, Volume 165, pp. 360 - 391

Using a result of Gessel and Reutenauer, we find a simple formula for the number of cyclic permutations with a given descent set, by expressing it in terms of...

Descent set | Permutation | Cycle | MATHEMATICS | PATTERNS | Mathematics - Combinatorics

Descent set | Permutation | Cycle | MATHEMATICS | PATTERNS | Mathematics - Combinatorics

Journal Article

Mathematische Annalen, ISSN 0025-5831, 8/2019, Volume 374, Issue 3, pp. 1439 - 1457

In this paper we extend to algebraic cobordism the classical Damon–Kempf–Laksov formula, which expresses the Chow ring Schubert classes of Grassmann bundles as...

Mathematics, general | Secondary: 05E05 | Mathematics | 55N22 | 14C17 | Primary: 14M15 | MATHEMATICS | K-THEORY | COHOMOLOGY | DEGENERACY LOCI CLASSES | SCHUBERT CALCULUS

Mathematics, general | Secondary: 05E05 | Mathematics | 55N22 | 14C17 | Primary: 14M15 | MATHEMATICS | K-THEORY | COHOMOLOGY | DEGENERACY LOCI CLASSES | SCHUBERT CALCULUS

Journal Article

Selecta Mathematica, ISSN 1022-1824, 1/2017, Volume 23, Issue 1, pp. 15 - 37

We prove the crepant resolution conjecture for Donaldson–Thomas invariants of toric Calabi–Yau 3-orbifolds with transverse A-singularities.

05E05 | Mathematics, general | Mathematics | 14N35 | MATHEMATICS | MATHEMATICS, APPLIED | Contact lenses

05E05 | Mathematics, general | Mathematics | 14N35 | MATHEMATICS | MATHEMATICS, APPLIED | Contact lenses

Journal Article

Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2017, Volume 47, Issue 4, pp. 1259 - 1275

In this paper, we exhibit two matrix representations of the rational roots of generalized Fibonacci polynomials (GFPs) under convolution product, in terms of...

Weighted isobaric polynomials | Stirling operators | Matrix representation | Multiplicative arithmetic functions | Generalized fibonacci polynomials | SYMMETRIC POLYNOMIALS | MATHEMATICS | ARITHMETIC FUNCTIONS | FIELDS | RING | matrix representation | multiplicative arithmetic functions | generalized Fibonacci polynomials

Weighted isobaric polynomials | Stirling operators | Matrix representation | Multiplicative arithmetic functions | Generalized fibonacci polynomials | SYMMETRIC POLYNOMIALS | MATHEMATICS | ARITHMETIC FUNCTIONS | FIELDS | RING | matrix representation | multiplicative arithmetic functions | generalized Fibonacci polynomials

Journal Article

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 07/2019, Volume 2019, Issue 13, pp. 4047 - 4080

We prove a general theorem that gives a linear recurrence for tuples of paths in every cylindrical network. This can be seen as a cylindrical analog of the...

MATHEMATICS | PATHS | YOUNG TABLEAUX | FRIENDLY WALKERS | VICIOUS WALKERS | DETERMINANTS | Mathematics - Combinatorics

MATHEMATICS | PATHS | YOUNG TABLEAUX | FRIENDLY WALKERS | VICIOUS WALKERS | DETERMINANTS | Mathematics - Combinatorics

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2019, Volume 60, Issue 2, p. 23506

In 2008, Lehner, Wettig, Guhr, and Wei conjectured a power series identity and showed that it implied a determinantal formula for a Bessel-type integral over...

PHYSICS, MATHEMATICAL | Supersymmetry | Partitions | Integrals | Partitions (mathematics) | Quarks | Power series | Quantum chromodynamics

PHYSICS, MATHEMATICAL | Supersymmetry | Partitions | Integrals | Partitions (mathematics) | Quarks | Power series | Quantum chromodynamics

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 9/2019, Volume 35, Issue 5, pp. 1077 - 1090

The Eulerian distribution on the involutions of the symmetric group is unimodal, as shown by Guo and Zeng. In this paper we prove that the Eulerian...

Unimodality | Involution | Quasisymmetric function | 05A20 | 05E05 | Mathematics | Engineering Design | Combinatorics | 05A15 | Descent | Hyperoctahedral group | MATHEMATICS | Permutations | Group theory

Unimodality | Involution | Quasisymmetric function | 05A20 | 05E05 | Mathematics | Engineering Design | Combinatorics | 05A15 | Descent | Hyperoctahedral group | MATHEMATICS | Permutations | Group theory

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 12/2016, Volume 44, Issue 4, pp. 973 - 1007

We prove a conjecture of Knutson asserting that the Schubert structure constants of the cohomology ring of a two-step flag variety are equal to the number of...

Gromov–Witten invariants | Schubert calculus | 14M15 | Two-step flag manifolds | Mathematics | Puzzle | Littlewood–Richardson rule | Secondary 14N15 | Convex and Discrete Geometry | Primary 05E05 | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Quantum cohomology of Grassmannians | Combinatorics | Computer Science, general | Littlewood-Richardson rule | MATHEMATICS | GRASSMANNIANS | Gromov-Witten invariants | VARIETIES | SCHUBERT POLYNOMIALS | School facilities | Algorithms | Education parks

Gromov–Witten invariants | Schubert calculus | 14M15 | Two-step flag manifolds | Mathematics | Puzzle | Littlewood–Richardson rule | Secondary 14N15 | Convex and Discrete Geometry | Primary 05E05 | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Quantum cohomology of Grassmannians | Combinatorics | Computer Science, general | Littlewood-Richardson rule | MATHEMATICS | GRASSMANNIANS | Gromov-Witten invariants | VARIETIES | SCHUBERT POLYNOMIALS | School facilities | Algorithms | Education parks

Journal Article

European Journal of Combinatorics, ISSN 0195-6698, 01/2019, Volume 75, pp. 172 - 194

We prove a combinatorial formula for Macdonald cumulants which generalizes the celebrated formula of Haglund, Haiman and Loehr for Macdonald polynomials. We...

MATHEMATICS | COMBINATORIAL FORMULA | MODEL | POSITIVITY | Mathematics - Combinatorics

MATHEMATICS | COMBINATORIAL FORMULA | MODEL | POSITIVITY | Mathematics - Combinatorics

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 02/2014, Volume 163, Issue 3, pp. 513 - 563

We establish a fundamental connection between the geometric Robinson-Schensted-Knuth (RSK) correspondence and GL(N,R)-Whittaker functions, analogous to the...

MATHEMATICS | DIMENSIONAL DIRECTED POLYMER | SHAPE | RANDOM-WALKS | FLUCTUATIONS | PERCOLATION | PATHS | ASYMPTOTICS | MODEL | 05E05 | 60B20 | 05E10 | 82B23

MATHEMATICS | DIMENSIONAL DIRECTED POLYMER | SHAPE | RANDOM-WALKS | FLUCTUATIONS | PERCOLATION | PATHS | ASYMPTOTICS | MODEL | 05E05 | 60B20 | 05E10 | 82B23

Journal Article

Selecta Mathematica, ISSN 1022-1824, 4/2018, Volume 24, Issue 2, pp. 751 - 874

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for...

Secondary 05E05 | Mathematics, general | Mathematics | Primary 60K35 | 82B23 | ORTHOGONAL POLYNOMIAL ENSEMBLES | MATHEMATICS | YANG-BAXTER EQUATION | MATHEMATICS, APPLIED | RANDOM-WALKS | DYNAMICS | DUALITY | SYSTEMS

Secondary 05E05 | Mathematics, general | Mathematics | Primary 60K35 | 82B23 | ORTHOGONAL POLYNOMIAL ENSEMBLES | MATHEMATICS | YANG-BAXTER EQUATION | MATHEMATICS, APPLIED | RANDOM-WALKS | DYNAMICS | DUALITY | SYSTEMS

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 01/2019, Volume 223, Issue 1, pp. 395 - 421

Let V be a finite-dimensional representation of the complex circle C× determined by a weight vector a∈Zn. We study the Hilbert series Hilba(t) of the graded...

MATHEMATICS | MATHEMATICS, APPLIED | POLYTOPES | COHEN-MACAULAY | TORI | RINGS | Algebra

MATHEMATICS | MATHEMATICS, APPLIED | POLYTOPES | COHEN-MACAULAY | TORI | RINGS | Algebra

Journal Article

Selecta Mathematica, ISSN 1022-1824, 12/2019, Volume 25, Issue 5, pp. 1 - 37

A polynomial has saturated Newton polytope (SNP) if every lattice point of the convex hull of its exponent vectors corresponds to a monomial. We compile...

05E05 | Mathematics, general | 05E10 | Mathematics

05E05 | Mathematics, general | 05E10 | Mathematics

Journal Article

Annals of Combinatorics, ISSN 0218-0006, 6/2018, Volume 22, Issue 2, pp. 347 - 361

The immaculate functions, $${\mathfrak{S}_a}$$ Sa , were introduced as a Schur-like basis for NSym, the ring of noncommutative symmetric functions. We...

05E05 | Schur functions | Mathematics | non-commutative symmetric functions | Combinatorics | tableaux

05E05 | Schur functions | Mathematics | non-commutative symmetric functions | Combinatorics | tableaux

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2018, Volume 290, Issue 3, pp. 1173 - 1197

We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young...

Hypergeometric functions | 11M41 | Jacobi–Trudi formula | Hankel determinants | Multiple zeta values | Schur functions | 05E05 | Mathematics, general | Mathematics | 33C05 | MATHEMATICS | Jacobi-Trudi formula

Hypergeometric functions | 11M41 | Jacobi–Trudi formula | Hankel determinants | Multiple zeta values | Schur functions | 05E05 | Mathematics, general | Mathematics | 33C05 | MATHEMATICS | Jacobi-Trudi formula

Journal Article

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