Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index
Combinatorics
2026-02-04 v1
Abstract
We introduce a new class of Eulerian posets, called S-partitionable posets, which have a non-negative cd-index. These posets are a generalization of S-shellable complexes introduced by Stanley in 1994. We prove that S-partitionable posets have a non-negative cd-index via a recursive formula. Then, we introduce a semi-Eulerian version of S-partitionable posets, which we call SE-partitionable posets. We show that SE-partitionable posets also have a non-negative semi-Eulerian cd-index as defined by Juhnke-Kubitzke, Samper and Venturello in 2024.
Cite
@article{arxiv.2602.02913,
title = {Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index},
author = {Felipe Caster and Dan Guyer and José Alejandro Samper},
journal= {arXiv preprint arXiv:2602.02913},
year = {2026}
}
Comments
23 pages, 14 figures