Recursive Betti numbers for Cohen–Macaulay d -partite clutters arising from posets
| Autor: | Davide Bolognini |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
Mathematics::Commutative Algebra Betti number 010102 general mathematics 0102 computer and information sciences Extension (predicate logic) 01 natural sciences Combinatorics Simplicial complex Cover (topology) Integer 010201 computation theory & mathematics Bipartite graph Ideal (ring theory) 0101 mathematics Partially ordered set Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 220:3102-3118 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2016.02.006 |
| Popis: | A natural extension of bipartite graphs are d-partite clutters, where d≥2 is an integer. For a poset P, Ene, Herzog and Mohammadi introduced the d-partite clutter CP,d of multichains of length d in P, showing that it is Cohen–Macaulay. We prove that the cover ideal of CP,d admits an xi-splitting, determining a recursive formula for its Betti numbers and generalizing a result of Francisco, Ha and Van Tuyl on the cover ideal of Cohen–Macaulay bipartite graphs. Moreover we prove a Betti splitting result for the Alexander dual of a Cohen–Macaulay simplicial complex. Interesting examples are given, in particular the first example of ideal that does not admit Betti splitting in any characteristic. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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