A Generalized Macaulay Theorem and Generalized Face Rings
| dc.creator | Nevo, Eran | |
| dc.date | 2005-05-16 | |
| dc.date | 2006-02-23 | |
| dc.date.accessioned | 2026-07-07T06:39:57Z | |
| dc.date.available | 2026-07-07T06:39:57Z | |
| dc.description | We prove that the $f$-vector of members in a certain class of meet semi-lattices satisfies Macaulay inequalities. We construct a large family of meet semi-lattices belonging to this class, which includes all posets of multicomplexes, as well as meet semi-lattices with the "diamond property", discussed by Wegner, as spacial cases. Specializing the proof to that later family, one obtains the Kruskal-Katona inequalities and their proof as in Wegner's. For geometric meet semi lattices we construct an analogue of the exterior face ring, generalizing the classic construction for simplicial complexes. For a more general class, which include also multicomplexes, we construct an analogue of the Stanley-Reisner ring. These two constructions provide algebraic counterparts (and thus also algebraic proofs) of Kruskal-Katona's and Macaulay's inequalities for these classes, respectively. | |
| dc.description | Final version: 13 pages, 2 figures. Improved presentation, more detailed proofs, same results. To appear in JCTA | |
| dc.identifier | https://arxiv.org/abs/math/0505330 | |
| dc.identifier | http://arxiv.org/abs/math/0505330 | |
| dc.identifier | JCTA 113 (2006) 1321-1331 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101274 | |
| dc.subject | Combinatorics | |
| dc.subject | 06A12; 13F55 | |
| dc.title | A Generalized Macaulay Theorem and Generalized Face Rings | |
| dc.type | text |