Sum complexes - a new family of hypertrees
| dc.creator | Linial, Nathan | |
| dc.creator | Meshulam, Roy | |
| dc.creator | Rosenthal, Mishael | |
| dc.date | 2009-03-07 | |
| dc.date.accessioned | 2026-07-07T12:50:19Z | |
| dc.date.available | 2026-07-07T12:50:19Z | |
| dc.description | A k-dimensional hypertree X is a k-dimensional complex on n vertices with a full (k-1)-dimensional skeleton and \binom{n-1}{k} facets such that H_k(X;Q)=0. Here we introduce the following family of simplicial complexes. Let n,k be integers with k+1 and n relatively prime, and let A be a (k+1)-element subset of the cyclic group Z_n. The sum complex X_A is the pure k-dimensional complex on the vertex set Z_n whose facets are subsets σof Z_n such that |σ|=k+1 and \sum_{x \in σ}x \in A. It is shown that if n is prime then the complex X_A is a k-hypertree for every choice of A. On the other hand, for n prime X_A is k-collapsible iff A is an arithmetic progression in Z_n. | |
| dc.description | 18 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0903.1359 | |
| dc.identifier | http://arxiv.org/abs/0903.1359 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222648 | |
| dc.subject | Combinatorics | |
| dc.subject | 13F55; 55U10 | |
| dc.title | Sum complexes - a new family of hypertrees | |
| dc.type | text |