On cobweb posets tilling problem
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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 entails natural enquires already formulated therein. In our paper 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 dened below.
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 entails natural enquires already formulated therein. In our paper 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 dened below.
참고문헌 (7)
- Maciej Dziemia¶nczuk, "On Cobweb posets tiling problem", ~
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- A. K. Kwasniewski, "Cobweb posets as noncommutative prefabs", Advanced Studies in Contemporary Mathematics, 14(1), pp.37~47 (2007), 장전수학회(章田數學會)
- A. Krzysztof Kwa¶sniewski, "On cobweb posets and their combinatorially ad- missible sequences", ~ (2005)
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- Eduard Lucas, "Thorie des Fonctions Numriques Simplement Priodiques", American Journal of Mathematics, 1, pp.184~240 (1878)