A Meshalkin theorem for projective geometries
| dc.creator | Beck, Matthias | |
| dc.creator | Zaslavsky, Thomas | |
| dc.date | 2001-12-07 | |
| dc.date | 2003-07-01 | |
| dc.date.accessioned | 2026-07-07T04:45:04Z | |
| dc.date.available | 2026-07-07T04:45:04Z | |
| dc.description | Let M be a family of sequences (a_1,...,a_p) where each a_k is a flat in a projective geometry of rank n (dimension n-1) and order q, and the sum of ranks, r(a_1) + ... + r(a_p), equals the rank of the join a_1 v ... v a_p. We prove upper bounds on |M| and corresponding LYM inequalities assuming that (i) all joins are the whole geometry and for each k<p the set of all a_k's of sequences in M contains no chain of length l, and that (ii) the joins are arbitrary and the chain condition holds for all k. These results are q-analogs of generalizations of Meshalkin's and Erdos's generalizations of Sperner's theorem and their LYM companions, and they generalize Rota and Harper's q-analog of Erdos's generalization. | |
| dc.description | 8 pages, added journal reference | |
| dc.identifier | https://arxiv.org/abs/math/0112069 | |
| dc.identifier | http://arxiv.org/abs/math/0112069 | |
| dc.identifier | Journal of Combinatorial Theory Series A 102 (2003), 433-441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62838 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D05, 51E20; 06A07 | |
| dc.title | A Meshalkin theorem for projective geometries | |
| dc.type | text |