On Cobweb posets tiling problem
arXiv:0709.4263
Abstract
Kwasniewski's cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation was derived in the source papers and it entailes natural enquieres already formulated therein. In our note we response to one of those problems. This is a tiling problem. Our observations on tiling problem include proofs of tiling's existence for some cobweb-admissible sequences. We show also that not all cobwebs admit tiling as defined below.
15 pages, 15 figures
Cited by in corpus (7)
- On Cobweb Posets and Discrete F-Boxes Tilings
- On cobweb posets most relevant codings
- On multi F-nomial coefficients and Inversion formula for F-nomial coefficients
- Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients
- On natural join of posets properties and first applications
- Natural join construction of graded posets versus ordinal sum and discrete hyper boxes
- On Cobweb Admissible Sequences - The Production Theorem