Distributive Lattices, Bipartite Graphs and Alexander Duality
| dc.creator | Herzog, Juergen | |
| dc.creator | Hibi, Takayuki | |
| dc.date | 2003-07-17 | |
| dc.date.accessioned | 2026-07-07T04:59:43Z | |
| dc.date.available | 2026-07-07T04:59:43Z | |
| dc.description | A certain squarefree monomial ideal $H_P$ arising from a finite partially ordered set $P$ will be studied from viewpoints of both commutative algebra and combinatorics. First, it is proved that the defining ideal of the Rees algebra of $H_P$ possesses a quadratic Gröbner basis. Thus in particular all powers of $H_P$ have linear resolutions. Second, the minimal free graded resolution of $H_P$ will be constructed explicitly and a combinatorial formula to compute the Betti numbers of $H_P$ will be presented. Third, by using the fact that the Alexander dual of the simplicial complex $Δ$ whose Stanley--Reisner ideal coincides with $H_P$ is Cohen--Macaulay, all the Cohen--Macaulay bipartite graphs will be classified. | |
| dc.identifier | https://arxiv.org/abs/math/0307235 | |
| dc.identifier | http://arxiv.org/abs/math/0307235 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68099 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 13F55, 13H10, 06A07, 06D99, 05C99 | |
| dc.title | Distributive Lattices, Bipartite Graphs and Alexander Duality | |
| dc.type | text |