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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
Journal Article
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
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
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
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
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
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
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
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
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
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
Journal Article
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
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
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
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
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
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
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
Journal Article
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