Results 21 to 30 of about 55 (53)

On the $\operatorname{rix}$ statistic and valley-hopping [PDF]

Discrete Mathematics & Theoretical Computer Science
This paper studies the relationship between the modified Foata$\unicode{x2013}$Strehl action (a.k.a. valley-hopping)$\unicode{x2014}$a group action on permutations used to demonstrate the $\gamma$-positivity of the Eulerian polynomials$\unicode{x2014 ...
Nadia Lafrenière, Yan Zhuang
doaj   +1 more source

GEOMETRIC BIJECTIONS FOR REGULAR MATROIDS, ZONOTOPES, AND EHRHART THEORY

Forum of Mathematics, Sigma, 2019
Let $M$ be a regular matroid. The Jacobian group $\text{Jac}(M)$ of $M$ is a finite abelian group whose cardinality is equal to the number of bases of $M$.
SPENCER BACKMAN, MATTHEW BAKER, CHI HO YUEN   +2 more
doaj   +1 more source

Rowmotion on \(m\)-Tamari and biCambrian lattices [PDF]

Thomas and Williams conjectured that rowmotion acting on the rational \((a,b)\)-Tamari lattice has order \(a+b-1\). We construct an equivariant bijection that proves this conjecture when \(a\equiv 1\pmod b\); in fact, we determine the entire orbit ...
Lin, James, Defant, Colin, Defant, Colin ; Lin, James   +2 more
core   +1 more source

Coloring Groups [PDF]

Discrete Mathematics & Theoretical Computer Science
We introduce coloring groups, which are permutation groups obtained from a proper edge coloring of a graph. These groups generalize the generalized toggle groups of Striker (which themselves generalize the toggle groups introduced by Cameron and Fon-der ...
Ben Adenbaum, Alexander Wilson
doaj   +1 more source

Viennot shadows and graded module structure in colored permutation groups [PDF]

Let \(\mathbf{x}_{n \times n}\) be a matrix of \(n \times n\) variables, and let \(\mathbb{C}[\mathbf{x}_{n \times n}]\) be the polynomial ring on these variables. Let \(\mathfrak{S}_{n,r}\) be the group of colored permutations, consisting of \({n \times
Liu, Jasper Moxuan
core   +1 more source

Classifying pentavalent symmetric graphs of order 12pq

Open Mathematics
A graph is said to be symmetric if its automorphism group is transitive on its arcs. Guo et al. (Pentavalent symmetric graphs of order 12p, Electron. J. Combin. 18 (2011), no. 1, #P233, DOI: https://doi.org/10.37236/720) and Ling (Classifying pentavalent
Qian Xiaorui, Ling Bo, Yang Jinlong, Zhao Yun   +3 more
doaj   +1 more source

Bender–Knuth Billiards in Coxeter Groups

Forum of Mathematics, Sigma
Let $(W,S)$ be a Coxeter system, and write $S=\{s_i:i\in I\}$ , where I is a finite index set. Fix a nonempty convex subset $\mathscr {L}$ of W. If W is of type A, then $\mathscr {L}$ is the set of linear extensions of a poset,
Grant Barkley, Colin Defant, Eliot Hodges, Noah Kravitz, Mitchell Lee   +4 more
doaj   +1 more source

Orthogonal roots, Macdonald representations, and quasiparabolic sets

Forum of Mathematics, Sigma
Let W be a simply laced Weyl group of finite type and rank n. If W has type $E_7$ , $E_8$ or $D_n$ for n even, then the root system of W has subsystems of type $nA_1$ .
R. M. Green, Tianyuan Xu
doaj   +1 more source

Equivariant Ehrhart theory of hypersimplices

Forum of Mathematics, Sigma
We study the hypersimplex under the action of the symmetric group $S_n$ by coordinate permutation. We prove that its equivariant volume, given by the evaluation of its equivariant $H^*$ -series at $1$ , is the permutation character of ...
Oliver Clarke, Max Kölbl
doaj   +1 more source

Finding lower bounds on the growth and entropy of subshifts over countable groups

Mathematics Subject Classification 2020: 37B10 (primary); 05E18 (secondary)International audienceWe provide a lower bound on the growth of a subshift based on a simple condition on the set of forbidden patterns defining that subshift.
Rosenfeld, Matthieu
core   +1 more source