3 citations · 16 across the 12 of their papers we have counts for
16 papers · 1 filter
Promotion permutations for tableaux
Christian Gaetz, Oliver Pechenik, Stephan Pfannerer +2
In our companion paper, we develop a new -web basis. Basis elements are given by certain planar graphs and are constructed so that important algebraic operations can be perfo…
Rotation-invariant web bases from hourglass plabic graphs
Christian Gaetz, Oliver Pechenik, Stephan Pfannerer +2
Webs give a diagrammatic calculus for spaces of tensor invariants. We introduce hourglass plabic graphs as a new avatar of webs, and use these to give the first rotation-invariant…
Cyclotomic generating functions
Sara C. Billey, Joshua P. Swanson
It is a remarkable fact that for many statistics on finite sets of combinatorial objects, the roots of the corresponding generating function are each either a complex root of unity…
q-Stirling numbers in type B
Bruce E. Sagan, Joshua P. Swanson
Stirling numbers, which count partitions of a set and permutations in the symmetric group, have found extensive application in combinatorics, geometry, and algebra. We study analog…
Curious cyclic sieving on increasing tableaux
Christian Gaetz, Oliver Pechenik, Jessica Striker +1
We prove a cyclic sieving result for the set of packed increasing tableaux with maximum entry under K-promotion. The "curiosity" is that the sieving polynomi…
Harmonic differential forms for pseudo-reflection groups II. Bi-degree bounds
Joshua P. Swanson, Nolan R. Wallach
This paper studies three results that describe the structure of the super-coinvariant algebra of pseudo-reflection groups over a field of characteristic . Our most general resul…
Tanisaki witness relations for harmonic differential forms
Joshua P. Swanson
Inspired by a series of conjectures related to higher coinvariant algebras, we present two families of relations involving harmonic differential forms of the symmetric group. Our r…
The metric space of limit laws for -hook formulas
Sara C. Billey, Joshua P. Swanson
In earlier work, Billey--Konvalinka--Swanson studied the asymptotic distribution of the coefficients of Stanley's -hook length formula, or equivalently the major index on standa…
On the distribution of the major index on standard Young tableaux
Sara C. Billey, Matjaž Konvalinka, Joshua P. Swanson
The study of permutation and partition statistics is a classical topic in enumerative combinatorics. The major index statistic on permutations was introduced a century ago by Percy…
Harmonic differential forms for pseudo-reflection groups I. Semi-invariants
Joshua P. Swanson, Nolan R. Wallach
We give a type-independent construction of an explicit basis for the semi-invariant harmonic differential forms of an arbitrary pseudo-reflection group in characteristic zero. Our…
Alternating super-polynomials and super-coinvariants of finite reflection groups
Joshua P Swanson
Motivated by a recent conjecture of Zabrocki, Wallach described the alternants in the super-coinvariant algebra of the symmetric group in one set of commuting and one set of anti-c…
Asymptotic normality of the major index on standard tableaux
Sara C. Billey, Matjaž Konvalinka, Joshua P. Swanson
We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for a…
On a theorem of Baxter and Zeilberger via a result of Roselle
Joshua P. Swanson
We provide a new proof of a result of Baxter and Zeilberger showing that inv and maj on permutations are jointly independently asymptotically normally distributed. The main feature…
Cyclic sieving, necklaces, and branching rules related to Thrall's problem
Connor Ahlbach, Joshua P. Swanson
We show that the cyclic sieving phenomenon of Reiner--Stanton--White together with necklace generating functions arising from work of Klyachko offer a remarkably unified, direct, a…
Refined Cyclic Sieving on Words for the Major Index Statistic
Connor Ahlbach, Joshua Swanson
Reiner-Stanton-White defined the cyclic sieving phenomenon (CSP) associated to a finite cyclic group action and a polynomial. A key example arises from the length generating functi…
On the Existence of Tableaux with Given Modular Major Index
Joshua P. Swanson
We provide simple necessary and sufficient conditions for the existence of a standard Young tableau of a given shape and major index mod , for all . Our result generalize…