Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918320695934976 |
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| author | Caster, Felipe Guyer, Dan Samper, José Alejandro |
| author_facet | Caster, Felipe Guyer, Dan Samper, José Alejandro |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_02913 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index Caster, Felipe Guyer, Dan Samper, José Alejandro Combinatorics 52B05, 05E45, 06A07 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. |
| title | Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index |
| topic | Combinatorics 52B05, 05E45, 06A07 |
| url | https://arxiv.org/abs/2602.02913 |