On Cobweb posets tiling problem

Details On Cobweb posets tiling problem On Cobweb posets tiling problem

2007-09-26

arxiv.org/abs/0709.4263v2

Adv. Stud. Contemp. Math. volume 16 (2), 2008 (April) pp. 219-233

Mathematics

Combinatorics

15 pages, 15 figures

Scientific paper

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.

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