David E Speyer

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20232026

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5 papers · 1 filter

math.CO2026

L-log-concavity and a proof of the conjecture of Lam, Postnikov and Pylyavskyy

David E Speyer

Let $λ$ , $μ$ , $λ^{'}$ , $μ^{'}$ be partitions. The conjecture of Lam, Postnikov and Pylyavskyy states that, if $λ + μ = λ^{'} + μ^{'}$ , and $\min(λ_i-λ_j, μ_i-μ_j) \leq λ'_i - λ'_j \leq \max(λ_i-λ…

math.CO2025

Extended Weak Order for the Rank 3 Universal Coxeter Group

Grant Barkley, Colin Defant, Patricia Hersh +3

The weak order is a classical poset structure on a Coxeter group; it is a lattice when the group is finite but merely a meet-semilattice when the group is infinite. Motivated by pr…

math.CO2025

Rowmotion and Echelonmotion

Colin Defant, Yuhan Jiang, Rene Marczinzik +4

Given a linear extension $σ$ of a finite poset $R$ , we consider the permutation matrix indexing the Schubert cell containing the Cartan matrix of $R$ with respect to $σ$ . This yiel…

math.CO2024

The omega invariant of a matroid

Alex Fink, Kris Shaw, David E Speyer

The third author introduced the $g$ -polynomial $g_{M} (t)$ of a matroid, a covaluative matroid statistic which is unchanged under series and parallel extension. The $g$ -polynomial of…

math.CO2023

Affine extended weak order is a lattice

Grant T. Barkley, David E Speyer

Coxeter groups are equipped with a partial order known as the weak order, such that $u \leq v$ if the inversions of $u$ are a subset of the inversions of $v$ . In finite Coxeter gro…