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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-Richardson rules… (More)

We say two posets are doppelgängers if they have the same number of P -partitions of each height k. We give a uniform framework for bijective proofs that posets are doppelgängers by synthesizing… (More)

The Hillman–Grassl correspondence is a well-known bijection between multisets of rim hooks of a partition shape λ and reverse plane partitions of λ. We use the tools of quiver representations to… (More)

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-theoretic analogues of… (More)

In this paper, we work toward answering the following question: given a uniformly random algebra homomorphism from the ring of symmetric functions over Z to a finite field Fq, what is the probability… (More)

- Zachary Hamaker, Adam Keilthy, +4 authors Shuqi Zhou

- Rebecca Patrias
- 2019

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 result of the… (More)

Abstract. Given an element in a finite-dimensional real vector space, V , that is a nonnegative linear combination of basis vectors for some basis B, we compute the probability that it is furthermore… (More)

We use Khovanov and Kuperberg’s web growth rules to identify the minimal term in the invariant associated to an SL3 web diagram, with respect to a particular term order.

- Susanna Fishel, Elizabeth Milicevic, Rebecca Patrias, Bridget Eileen Tenner
- Eur. J. Comb.
- 2018

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 permutation. We classify the… (More)