1 citations · 2 across the 8 of their papers we have counts for
9 papers
Dot actions and Hessenberg spaces for dihedral groups
Jonathan Boretsky, Reuven Hodges, Nathan Lesnevich +2
Splines on Weyl groups model the equivariant cohomology of regular semisimple Hessenberg varieties, and the natural group action on them encodes the monodromy action. The resulting…
Shifted lower Bruhat intervals are EL-shellable
Aman Dave, Taiwen Feng, Nathan Lesnevich +4
Let be an arbitrary Coxeter group. The shifted Bruhat interval , the translate of the Bruhat interval by an element , is partially ordered by…
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}(σ_1 \preceq_W σ_2)=\…
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…
Restricted inversion polynomials
Jeongwon Lee, Nathan Lesnevich, Martha Precup
For a finite subset of positive integers, the descent polynomial counts the number of permutations in that have descent set . We generalize descent…
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…
Splines on Cayley Graphs of the Symmetric Group
Nathan R. T. Lesnevich
A spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belon…
Hook-Shape Immanant Characters from Stanley-Stembridge Characters
Nathan R. T. Lesnevich
We consider the Schur-positivity of monomial immanants of Jacobi-Trudi matrices, in particular whether a non-negative coefficient of the trivial Schur function implies non-negative…
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 -partition enumerators is -positive, i.e., positive in Gessel's fundamen…