18 citations · 71 across the 15 of their papers we have counts for
21 papers
Staircase diagrams, pattern avoidance, and smooth permutations
Faqruddin Ali Azam, Edward Richmond
A well known result due to Lakshmibai and Sandhya states that smooth Schubert varieties of type A correspond to permutations that avoid the patterns 3412 and 4231. It was later sho…
Shifted lower Bruhat intervals are EL-shellable
Aman Dave, Taiwen Feng, Nathan Lesnevich +4
Let be an arbitrary Coxeter group. The shifted Bruhat interval , the translate of the Bruhat interval by an element , is partially ordered by…
Demazure product of permutations and hopping
Tina Li, Suho Oh, Edward Richmond +2
The Demazure product (also goes by the name of 0-Hecke product or the greedy product) is an associative operation on Coxeter groups with interesting properties and important applic…
The Isomorphism Problem for cominuscule Schubert Varieties
Edward Richmond, Mihail Tarigradschi, Weihong Xu
Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of roots labeled long/short. These la…
The parabolic coset structure of Bruhat intervals in Coxeter groups
Suho Oh, Edward Richmond
In this paper, we study the decomposition of Bruhat intervals in a Coxeter group with respect to cosets of a parabolic subgroup. Our main result is that the intersection of a lower…
On the generating function for intervals in Young's lattice
Faqruddin Azam, Edward Richmond
In this paper, we study a family of generating functions whose coefficients are polynomials that enumerate partitions in lower order ideals of Young's lattice. Our main result is t…
The isomorphism problem for Schubert varieties
Edward Richmond, William Slofstra
Schubert varieties in the full flag variety of Kac-Moody type are indexed by elements of the corresponding Weyl group. We give a practical criterion for when two such Schubert vari…
An equivariant basis for the cohomology of Springer fibers
Martha Precup, Edward Richmond
Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this paper, we analyze the equivariant coh…
Noncommutative LR coefficients and crystal reflection operators
Edward Richmond, Vasu Tewari
We relate noncommutative Littlewood-Richardson coefficients of Bessenrodt-Luoto-van Willigenburg to classical Littlewood-Richardson coefficients via crystal reflection operators. A…
The Nash blow-up of a cominuscule Schubert variety
Edward Richmond, William Slofstra, Alexander Woo
We compute the Nash blow-up of a cominuscule Schubert variety. In particular, we show that the Nash blow-up is algebraically isomorphic to another Schubert variety of the same Lie…
Smooth Schubert varieties in the affine flag variety of type
Edward Richmond, William Slofstra
We show that every smooth Schubert variety of affine type is an iterated fibre bundle of Grassmannians, extending an analogous result by Ryan and Wolper for Schubert va…
Pattern avoidance and fiber bundle structures on Schubert varieties
Timothy Alland, Edward Richmond
We give a permutation pattern avoidance criteria for determining when the projection map from the flag variety to a Grassmannian induces a fiber bundle structure on a Schubert vari…
Staircase diagrams and enumeration of smooth Schubert varieties
Edward Richmond, William Slofstra
We enumerate smooth and rationally smooth Schubert varieties in the classical finite types A, B, C, and D, extending Haiman's enumeration for type A. To do this enumeration, we int…
Billey-Postnikov decompositions and the fibre bundle structure of Schubert varieties
Edward Richmond, William Slofstra
A theorem of Ryan and Wolper states that a type A Schubert variety is smooth if and only if it is an iterated fibre bundle of Grassmannians. We extend this theorem to arbitrary fin…
Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians
David Anderson, Edward Richmond, Alexander Yong
The saturation theorem of [Knutson-Tao '99] concerns the nonvanishing of Littlewood-Richardson coefficients. In combination with work of [Klyachko '98], it implies [Horn '62]'s con…
Rationally smooth elements of Coxeter groups and triangle group avoidance
Edward Richmond, William Slofstra
We study a family of infinite-type Coxeter groups defined by the avoidance of certain rank 3 parabolic subgroups. For this family, rationally smooth elements can be detected by loo…
A combinatorial characterization of tight fusion frames
Marcin Bownik, Kurt Luoto, Edward Richmond
In this paper we give a combinatorial characterization of tight fusion frame (TFF) sequences using Littlewood-Richardson skew tableaux. The equal rank case has been solved recently…
Littlewood-Richardson coefficients for reflection groups
Arkady Berenstein, Edward Richmond
In this paper we explicitly compute all Littlewood-Richardson coefficients for semisimple or Kac-Moody groups G, that is, the structure coefficients of the cohomology algebra H^*(G…
Branching Schubert calculus and the Belkale-Kumar product on cohomology
Nicolas Ressayre, Edward Richmond
In 2006, Belkale and Kumar define a new product on the cohomology of flag varieties and use this new product to give an improved solution to the eigencone problem for complex reduc…
A multiplicative formula for structure constants in the cohomology of flag varieties
Edward Richmond
Let G be a complex semi-simple Lie group and let P,Q be a pair of parabolic subgroups of G such that Q contains P. Consider the flag varieties G/P, G/Q and Q/P. We show that certai…
A partial Horn recursion in the cohomology of flag varieties
Edward Richmond
Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterize…