Associated Primes of the Square of the Alexander Dual of Hypergraphs
| dc.creator | Cutkosky, Ashok | |
| dc.date | 2009-01-12 | |
| dc.date.accessioned | 2026-07-07T12:28:52Z | |
| dc.date.available | 2026-07-07T12:28:52Z | |
| dc.description | The purpose of this paper is to provide methods for determining the associated primes of the square of the Alexander dual of the edge ideal for an m-hypergraph H. We prove a general method for detecting associated primes of the square of the Alexander dual of the edge ideal based on combinatorial conditions on the m-hypergraph. Also, we demonstrate a more efficient combinatorial criterion for detecting the non-existence of non-minimal associated primes. In investigating 3-hypergraphs, we prove a surprising extension of the previously discovered results for 2-hypergraphs (simple graphs). For 2-hypergraphs, associated primes of the square of the Alexander dual of the edge ideal are either of height 2 or of odd height greater than 2. However, we prove that in the 3-hypergraph case, there is no such restriction - or indeed any restriction - on the heights of the associated primes. Further, we generalize this result to any dimension greater than 3. Specifically, given any integers m, q, and n with 3\leq m\leq q\leq n, we construct a m-hypergraph of size n with an associated prime of height q. We further prove that it is possible to construct connected m-hypergraphs under the same conditions. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0901.1678 | |
| dc.identifier | http://arxiv.org/abs/0901.1678 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215687 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 13F55; 05E99 | |
| dc.title | Associated Primes of the Square of the Alexander Dual of Hypergraphs | |
| dc.type | text |