62 citations · 348 across the 73 of their papers we have counts for
56 papers · 1 filter
Combinatorial commutative algebra rules
Ada Stelzer, Alexander Yong
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study…
Presenting the cohomology of a Schubert variety: Proof of the minimality conjecture
Avery St. Dizier, Alexander Yong
A minimal presentation of the cohomology ring of the flag manifold was given in [A. Borel, 1953]. This presentation was extended by [E. Akyildiz-A. Lascoux-P. Pragacz, 199…
Castelnuovo-Mumford regularity and Schubert geometry
Alexander Yong
We study the Castelnuovo-Mumford regularity of tangent cones of Schubert varieties. Conjectures about this statistic are presented; these are proved for the covexillary case. This…
Minimal equations for matrix Schubert varieties
Shiliang Gao, Alexander Yong
Explicit minimal generators for Fulton's Schubert determinantal ideals are determined along with some implications.
Classification of Levi-spherical Schubert varieties
Yibo Gao, Reuven Hodges, Alexander Yong
A Schubert variety in the complete flag manifold is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give…
An efficient algorithm for deciding vanishing of Schubert polynomial coefficients
Anshul Adve, Colleen Robichaux, Alexander Yong
Schubert polynomials form a basis of all polynomials and appear in the study of cohomology rings of flag manifolds. The vanishing problem for Schubert polynomials asks if a coeffic…
The "Grothendieck to Lascoux" conjecture
Victor Reiner, Alexander Yong
This report formulates a conjectural combinatorial rule that positively expands Grothendieck polynomials into Lascoux polynomials. It generalizes one such formula expanding Schuber…
The Kostka semigroup and its Hilbert basis
Shiliang Gao, Joshua Kiers, Gidon Orelowitz +1
The Kostka semigroup consists of pairs of partitions with at most r parts that have positive Kostka coefficient. For this semigroup, Hilbert basis membership is an NP-complete prob…
Proper permutations, Schubert geometry, and randomness
David Brewster, Reuven Hodges, Alexander Yong
We define and study proper permutations. Properness is a geometrically natural necessary criterion for a Schubert variety to be Levi-spherical. We prove the probability that a rand…
Generalized permutahedra and Schubert calculus
Avery St. Dizier, Alexander Yong
We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the flag variety. Our argument utili…
Newell-Littlewood numbers II: extended Horn inequalities
Shiliang Gao, Gidon Orelowitz, Alexander Yong
The Newell-Littlewood numbers are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions …
Multiplicity-free key polynomials
Reuven Hodges, Alexander Yong
The key polynomials, defined by A. Lascoux-M.-P. Schützenberger, are characters for the Demazure modules of type A. We classify multiplicity-free key polynomials. The proof uses tw…
Newell-Littlewood numbers
Shiliang Gao, Gidon Orelowitz, Alexander Yong
The Newell-Littlewood numbers are defined in terms of their celebrated cousins, the Littlewood-Richardson coefficients. Both arise as tensor product multiplicities for a classical…
Equivariant cohomology, Schubert calculus, and edge labeled tableaux
Colleen Robichaux, Harshit Yadav, Alexander Yong
This chapter concerns edge labeled Young tableaux, introduced by H. Thomas and the third author. It is used to model equivariant Schubert calculus of Grassmannians. We survey resul…
The A.B.C.Ds of Schubert calculus
Colleen Robichaux, Harshit Yadav, Alexander Yong
We collect Atiyah-Bott Combinatorial Dreams (A.B.C.Ds) in Schubert calculus. One result relates equivariant structure coefficients for two isotropic flag manifolds, with consequenc…
Reduced word enumeration, complexity, and randomization
Cara Monical, Benjamin Pankow, Alexander Yong
A reduced word of a permutation is a minimal length expression of as a product of simple transpositions. We examine the computational complexity, formulas and (randomized)…
Computational complexity, Newton polytopes, and Schubert polynomials
Anshul Adve, Colleen Robichaux, Alexander Yong
The nonvanishing problem asks if a coefficient of a polynomial is nonzero. Many families of polynomials in algebraic combinatorics admit combinatorial counting rules and simultaneo…
Tropicalization, symmetric polynomials, and complexity
Alexander Woo, Alexander Yong
D. Grigoriev-G. Koshevoy recently proved that tropical Schur polynomials have (at worst) polynomial tropical semiring complexity. They also conjectured tropical skew Schur polynomi…
Vanishing of Littlewood-Richardson polynomials is in P
Anshul Adve, Colleen Robichaux, Alexander Yong
J. DeLoera-T. McAllister and K. D. Mulmuley-H. Narayanan-M. Sohoni independently proved that determining the vanishing of Littlewood-Richardson coefficients has strongly polynomial…
Symmetric group representations and Z
Anshul Adve, Alexander Yong
We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluatio…
Newton polytopes and symmetric Grothendieck polynomials
Laura Escobar, Alexander Yong
Symmetric Grothendieck polynomials are inhomogeneous versions of Schur polynomials that arise in combinatorial -theory. A polynomial has saturated Newton polytope (SNP) if every…
Newton Polytopes in Algebraic Combinatorics
Cara Monical, Neriman Tokcan, Alexander Yong
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 instances of SNP in algebra…
Partition Identities and Quiver Representations
Richard Rimanyi, Anna Weigandt, Alexander Yong
We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A.…
Rhombic tilings and Bott-Samelson varieties
Laura Escobar, Oliver Pechenik, Bridget Eileen Tenner +1
S.~Elnitsky (1997) gave an elegant bijection between rhombic tilings of -gons and commutation classes of reduced words in the symmetric group on letters. P.~Magyar (1998) f…