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17 papers · 1 filter
Distribution of maxima and minima statistics on alternating permutations, Springer numbers, and avoidance of flat POPs
Tian Han, Sergey Kitaev, Philip B. Zhang
In this paper, we find distributions of the left-to-right maxima, right-to-left maxima, left-to-right minima and right-to-left-minima statistics on up-down and down-up permutations…
Joint distributions of statistics over permutations avoiding two patterns of length 3
Tian Han, Sergey Kitaev
Finding distributions of permutation statistics over pattern-avoiding classes of permutations attracted much attention in the literature. In particular, Bukata et al. found distrib…
Conflict-free connection number and independence number of a graph
Jing Wang, Meng Ji
An edge-colored graph is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The conflict-free…
Group Connectivity under -Edge-Connectivity
Miaomiao Han, Jiaao Li, Xueliang Li +1
Let be two distinct finite Abelian groups with . A fundamental theorem of Tutte shows that a graph admits a nowhere-zero -flow if and only if it admits a nowhere-…
Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids
Matthew H. Y. Xie, Philip B. Zhang
The equivariant Kazhdan-Lusztig polynomial of a matroid was introduced by Gedeon, Proudfoot, and Young. Gedeon conjectured an explicit formula for the equivariant Kazhdan-Lusztig p…
Multivariate Stable Eulerian Polynomials on Segmented Permutations
Philip B. Zhang, Xutong Zhang
Recently, Nunge studied Eulerian polynomials on segmented permutations, namely \emph{generalized Eulerian polynomials}, and further asked whether their coefficients form unimodal s…