M. Sherman-Bennett

activity

20182022

collaborators

6 papers

math.CO2022

Leclerc's conjecture on a cluster structure for type A Richardson varieties

Khrystyna Serhiyenko, Melissa Sherman-Bennett

Leclerc constructed a conjectural cluster structure on Richardson varieties in simply laced types using cluster categories. We show that in type A, his conjectural cluster structur…

math.CO2021

$k$ -positivity of dual canonical basis elements from 1324- and 2143-avoiding Kazhdan-Lusztig immanants

Sunita Chepuri, Melissa Sherman-Bennett

In this note, we show that certain dual canonical basis elements of $C [S L_{m}]$ are positive when evaluated on $k$ -positive matrices, matrices whose minors of size $k \times…

math.CO2020

Saturation of Newton polytopes of type A and D cluster variables

Amal Mattoo, Melissa Sherman-Bennett

We study Newton polytopes for cluster variables in cluster algebras $A (Σ)$ of types A and D. A famous property of cluster algebras is the Laurent phenomenon: each cluster…

math.CO2019

Cluster structures in Schubert varieties in the Grassmannian

K. Serhiyenko, M. Sherman-Bennett, L. Williams

In this article we explain how the coordinate ring of each (open) Schubert variety in the Grassmannian can be identified with a cluster algebra, whose combinatorial structure is en…

math.CO2018

Combinatorics of cluster structures in Schubert varieties

Khrystyna Serhiyenko, Melissa Sherman-Bennett, Lauren Williams

We give an explicit combinatorial description of cluster structures in Schubert varieties of the Grassmannian in terms of (target labelings of) Postnikov's plabic graphs. This desc…

math.CO2018

Combinatorics of $X$ -variables in finite type cluster algebras

Melissa Sherman-Bennett

We compute the number of $X$ -variables (also called coefficients) of a cluster algebra of finite type when the underlying semifield is the universal semifield. For classi…