On Cobweb Posets and Discrete F-Boxes Tilings
| dc.creator | Dziemianczuk, M. | |
| dc.date | 2008-02-24 | |
| dc.date | 2009-04-02 | |
| dc.date.accessioned | 2026-07-07T12:58:45Z | |
| dc.date.available | 2026-07-07T12:58:45Z | |
| dc.description | F-boxes defined in [6] as hyper-boxes in N^{\infty} discrete space were applied here for the geometric description of the cobweb posetes Hasse diagrams tilings. The F-boxes edges sizes are taken to be values of terms of natural numbers' valued sequence F. The problem of partitions of hyper-boxes represented by graphs into blocks of special form is considered and these are to be called F-tilings. The proof of such tilings' existence for certain sub-family of admissible sequences F is delivered. The family of F-tilings which we consider here includes among others F = Natural numbers, Fibonacci numbers, Gaussian integers with their corresponding F-nomial (Binomial, Fibonomial, Gaussian) coefficients. Extension of this tiling problem onto the general case multi F-nomial coefficients is here proposed. Reformulation of the present cobweb tiling problem into a clique problem of a graph specially invented for that purpose - is proposed here too. To this end we illustrate the area of our reconnaissance by means of the Venn type map of various cobweb sequences families. | |
| dc.description | 24 pages, 15 figures, Affiliated to The Internet Gian-Carlo Polish Seminar http://ii.uwb.edu.pl/akk/sem/sem_rota.htm | |
| dc.identifier | https://arxiv.org/abs/0802.3473 | |
| dc.identifier | http://arxiv.org/abs/0802.3473 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225349 | |
| dc.subject | Combinatorics | |
| dc.subject | Discrete Mathematics | |
| dc.subject | 05A10, 05A19, 11B83, 11B65 | |
| dc.title | On Cobweb Posets and Discrete F-Boxes Tilings | |
| dc.type | text |