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- 저자 : A. K. Kwaśniewski (검색결과 1 건)
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On cobweb posets and their combinatorially admissible sequences
A. K. Kwaśniewski 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.1
The purpose of this article is to pose three computational problems which are quite easily formulated for the new class of directed acyclic graphs interpreted as Hasse diagrams. The problems posed are not yet solved though are of crucial importance for the vast class of new partially ordered sets with joint combinatorial interpretation. These so called cobweb posets - are relatives of Fibonacci tree and are labeled by spe- cic number sequences - natural numbers sequence and Fibonacci sequence included. One presents here also a join combinatorial interpretation of those posets` F-nomial coecients which are computed with the so called cobweb admissible sequences. Cob- web posets and their natural subposets are graded posets, sometimes called a ranked posets. They are vertex partitioned into such antichains фn (where n is a nonnega- tive integer) that for each фn, all of the elements covering x are in фn+1 and all the elements covered by x are in фn. We shall call the фn the n - th- level. The cobweb posets may be identied with a chain of di-bicliques i.e. by denition - a chain of com- plete bipartite one direction digraphs. Any chain of relations is therefore obtainable from the cobweb poset chain of complete relations via deleting arcs in di-bicliques of the complete relations chain.
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