5 papers · 1 filter
Order polytopes of generalized snake posets are -real-rooted
Benjamin Braun, Aryaman Jal
Order polytopes for generalized snake posets were recently studied by von Bell et al. (2022), and are known to be unimodularly equivalent to strength-one flow polytopes for acyclic…
Positroidal aspects of non-nesting rook placements
Aryaman Jal
Rook matroids were recently introduced by the author and Alexandersson as matroids whose bases arise from certain restricted rook placements on a skew-shaped board. They were shown…
Real-rootedness of rook-Eulerian polynomials
Per Alexandersson, Aryaman Jal, Maena Quemener
We introduce rook-Eulerian polynomials, a generalization of the classical Eulerian polynomials arising from complete rook placements on Ferrers boards, and prove that they are real…
Rook matroids and log-concavity of -Eulerian polynomials
Per Alexandersson, Aryaman Jal
We define and study rook matroids, the bases of which correspond to non-nesting rook placements on a skew Ferrers board. We show that rook matroids are a subclass of both transvers…
Polyhedral combinatorics of bisectors
Aryaman Jal, Katharina Jochemko
For any polyhedral norm, the bisector of two points is a polyhedral complex. We study combinatorial aspects of this complex. We investigate the sensitivity of the presence of label…