Nathan R. T. Lesnevich

collaborators

6 papers

math.CO2026

Shifted lower Bruhat intervals are EL-shellable

Aman Dave, Taiwen Feng, Nathan Lesnevich +4

Let $W$ be an arbitrary Coxeter group. The shifted Bruhat interval $[w_{1}, w_{2}] x^{- 1}$ , the translate of the Bruhat interval $[w_{1}, w_{2}]$ by an element $x$ , is partially ordered by…

math.CO2026

Comparability in Bruhat orders

Jonathan Boretsky, Alvaro Cornejo, Reuven Hodges +3

We determine the sharp asymptotic scale of the probability that two uniformly random permutations are comparable in weak Bruhat order, showing that $\mathbb{P}(Ï_1 \preceq_W Ï_2)…

math.CO2025

Signed permutations and degree-one dot action representations for types B and C

Nathan R. T. Lesnevich

A spline is an assignment of polynomials to the vertices of a graph, where the difference of two polynomials along an edge must belong to the ideal labeling that edge. We consider…

math.CO2025

Restricted inversion polynomials

Jeongwon Lee, Nathan Lesnevich, Martha Precup

For a finite subset $I$ of positive integers, the descent polynomial $D (I; n)$ counts the number of permutations in $S_{n}$ that have descent set $I$ . We generalize descent…

math.CO2025

The poset of maximal tubings of the cycle graph is a lattice

Ben Adenbaum, Emily Barnard, Max Hlavacek +4

The poset of maximal tubings of a graph generalizes several well-known and remarkable partial orders. Notable examples include the weak Bruhat order and the Tamari lattice, posets…

math.CO2025

Positivity among P-partition generating functions

Nathan R. T. Lesnevich, Peter R. W. McNamara

We seek simple conditions on a pair of labeled posets that determine when the difference of their $(P, I ¨ )$ -partition enumerators is $F$ -positive, i.e., positive in Gessel's fundame…