Maciej Dziemianczuk

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Kwaśniewski’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(More)
Responding to Kwaśniewski’s cobweb posets’ problems posed in [3, 4] we present here some results on one of them namely on Cobweb Tiling Problem. Kwaśniewski cobweb posets with tiling property are designated-coded by their correspondent tiling sequences. We show that the family of all cobweb tiling sequences includes Natural numbers, Fibonacci numbers,(More)
In response to [7], we discover the looked for inversion formula for F -nomial coefficients. Before supplying its proof, we generalize F -nomial coefficients to multi F -nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form σPk1,k2,...,ks of layer 〈Φ1 → Φn〉. Then we(More)
Abstract F -boxes defined in [6] as hyper-boxes in N∞ discrete space were applied here for the geometric description of the cobweb posetes Hasse diagrams tilings. The F -boxes edges sizes are taken to be values of terms of natural numbers’ valued sequence F . The problem of partitions of hyper-boxes represented by graphs into blocks of special form is(More)
The so-called ζ-analogues of the Stirling numbers of the first and second kind are considered. These numbers cover ordinary binomial and Gaussian coefficients, p, qStirling numbers and other combinatorial numbers studied with the help of object selection, Ferrers diagrams and rook theory. Our generalization includes these and now also the p, q-binomial(More)
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(α) are considered. For such specific sequences a new interpretation with respect to Kwaśniewski general(More)