Ilaria Seidel | Searcharxiv

arXiv2023

Periodic Points of Consecutive-Pattern-Avoiding Stack-Sorting Maps

West's stack-sorting map involves a stack which avoids the permutation $21$ consecutively. Defant and Zheng extended this to a consecutive-pattern-avoiding stack-sorting map $SC_σ$, where the stack must always avoid a given permutation $σ$ consecutively. We address one of the main conjectures raised by Defant and Zheng in their dynamical approach to $SC_σ$. Specifically, we show that the periodic points of $SC_σ$ are precisely the permutations that consecutively avoid $σ$ and its reverse.

math.CO↗

arXiv2020

The Rank-Generating Functions of Upho Posets

Upper homogeneous finite type (upho) posets are a large class of partially ordered sets with the property that the principal order filter at every vertex is isomorphic to the whole poset. Well-known examples include k-array trees, the grid graphs, and the Stern poset. Very little is known about upho posets in general. In this paper, we construct upho posets with Schur-positive Ehrenborg quasisymmetric functions, whose rank-generating functions have rational poles and zeros. We also categorize the rank-generating functions of all planar upho posets. Finally, we prove the existence of an upho poset with uncomputable rank-generating function.

math.CO↗