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arXiv · 0901.1337

Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients

M. Dziemianczuk
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Abstract

F-nomial coefficients encompass among others well-known binomial coefficients or Gaussian coefficients that count subsets of finite set and subspaces of finite vector space respectively. Here, the so called F-cobweb tiling sequences N(a) are considered. For such specific sequences a new interpretation with respect to Kwasniewski general combinatorial interpretation of F-nomial coefficients is unearhed. Namely, for tiling sequences F = N(a)$ the F-nomial coefficients are equal to the number of labeled special bipartite multigraphs denoted here as a-multigraphs G(a,n,k). An explicit relation between the number of k-colored a-multigraphs and multi N(a)-nomial coefficients is established. We also prove that the unsigned values of the first row of inversion matrix for N(a) -nomial coefficients considered here are equal to the numbers of directed acyclic a-multigraphs with n nodes.

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BibTeXRIS

M. Dziemianczuk. 2009-01-11. Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients. https://arxiv.org/abs/0901.1337

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