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arXiv · 2602.02913

Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index

Felipe Caster·Dan Guyer·José Alejandro Samper
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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.

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Felipe Caster, Dan Guyer, José Alejandro Samper. 2026-02-02. Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index. https://arxiv.org/abs/2602.02913

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