14 citations · 57 across the 17 of their papers we have counts for
23 papers
Promotion digraphs
Rebecca Patrias, Oliver Pechenik, Jessica Striker
Work of Gaetz, Pechenik, Pfannerer, Striker, and Swanson (2024) introduced promotion permutations for a rectangular standard Young tableau . These promotion permutations encode…
Web invariants for flamingo Specht modules
Chris Fraser, Rebecca Patrias, Oliver Pechenik +1
Webs yield an especially important realization of certain Specht modules, irreducible representations of symmetric groups, as they provide a pictorial basis with a convenient diagr…
A web basis of invariant polynomials from noncrossing partitions
Rebecca Patrias, Oliver Pechenik, Jessica Striker
The irreducible representations of symmetric groups can be realized as certain graded pieces of invariant rings, equivalently as global sections of line bundles on partial flag var…
Tableau evacuation and webs
Rebecca Patrias, Oliver Pechenik
Webs are certain planar diagrams embedded in disks. They index and describe bases of tensor products of representations of and . There are explic…
Set-valued domino tableaux and shifted set-valued domino tableaux
Florence Maas-Gariépy, Rebecca Patrias
We prove K-theoretic and shifted K-theoretic analogues of the bijection of Stanton and White between domino tableaux and pairs of semistandard tableaux. As a result, we obtain prod…
Path-cordial abelian groups
Rebecca Patrias, Oliver Pechenik
A labeling of the vertices of a graph by elements of any abelian group induces a labeling of the edges by summing the labels of their endpoints. Hovey defined the graph to…
Dynamics of plane partitions: Proof of the Cameron-Fon-Der-Flaass conjecture
Rebecca Patrias, Oliver Pechenik
One of the oldest outstanding problems in dynamical algebraic combinatorics is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995). Consider a plane partition i…
Minuscule reverse plane partitions via quiver representations
Alexander Garver, Rebecca Patrias, Hugh Thomas
The Hillman--Grassl correspondence is a well-known bijection between multisets of rim hooks of a partition shape and reverse plane partitions of . We use the tools of quiver…
Leading terms of web invariants
Véronique Bazier-Matte, Guillaume Douville, Alexander Garver +3
We use Khovanov and Kuperberg's web growth rules to identify the minimal term in the invariant associated to an web diagram, with respect to a particular term order.
Minuscule reverse plane partitions via quiver representations
Alexander Garver, Rebecca Patrias, Hugh Thomas
A nilpotent endomorphism of a quiver representation induces a linear transformation on the vector space at each vertex. Generically among all nilpotent endomorphisms, there is a we…
The probability of positivity in symmetric and quasisymmetric functions
Rebecca Patrias, Stephanie van Willigenburg
Given an element in a finite-dimensional real vector space, , that is a nonnegative linear combination of basis vectors for some basis , we compute the probability that it is…
What is Schur positivity and how common is it?
Rebecca Patrias
This is a short note about Schur positivity. We introduce Schur polynomials and explain how they appear in the representation theory of the general linear group. We end with a new…
Promotion on Generalized Oscillating Tableaux and Web Rotation
Rebecca Patrias
We introduce the notion of a generalized oscillating tableau and define a promotion operation on such tableaux that generalizes the classical promotion operation on standard Young…
Greene--Kleitman invariants for Sulzgruber insertion
Alexander Garver, Rebecca Patrias
R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets o…
Enumerations relating braid and commutation classes
Susanna Fishel, Elizabeth Milićević, Rebecca Patrias +1
We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutatio…
Jacobi-Trudi determinants over finite fields
Ben Anzis, Shuli Chen, Yibo Gao +3
In this paper, we work toward answering the following question: given a uniformly random algebra homomorphism from the ring of symmetric functions over the integers to a finite fie…
Coincidences among skew dual stable Grothendieck polynomials
Ethan Alwaise, Shuli Chen, Alexander Clifton +4
The question of when two skew Young diagrams produce the same skew Schur function has been well-studied. We investigate the same question in the case of stable Grothendieck polynom…
Doppelgängers: Bijections of Plane Partitions
Zachary Hamaker, Rebecca Patrias, Oliver Pechenik +1
We say two posets are "doppelgängers" if they have the same number of -partitions of each height . We give a uniform framework for bijective proofs that posets are doppelgäng…
Shifted Hecke insertion and the K-theory of OG(n,2n+1)
Zachary Hamaker, Adam Keilthy, Rebecca Patrias +3
Patrias and Pylyavskyy introduced shifted Hecke insertion as an application of their theory of dual filtered graphs. We use shifted Hecke insertion to construct symmetric function…
Antipode formulas for some combinatorial Hopf algebras
Rebecca Patrias
Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that can be thought of…
Dual Filtered Graphs
Rebecca Patrias, Pavlo Pylyavskyy
We define a K-theoretic analogue of Fomin's dual graded graphs, which we call dual filtered graphs. The key formula in the definition is DU-UD= D + I. Our major examples are K-theo…
K-Knuth Equivalence for Increasing Tableaux
Christian Gaetz, Michelle Mastrianni, Rebecca Patrias +4
A K-theoretic analogue of RSK insertion and Knuth equivalence relations was first introduced in 2006 by Buch, Kresch, Shimozono, Tamvakis, and Yong. The resulting K-Knuth equivalen…
K-theoretic Poirier-Reutenauer bialgebra
Rebecca Patrias, Pavlo Pylyavskyy
We use the K-Knuth equivalence of Buch and Samuel to define a K-theoretic analogue of the Poirier-Reutenauer Hopf algebra. As an application, we rederive the K-theoretic Littlewood…