Maciej Dziemianczuk

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Responding to Kwa´sniewski's cobweb posets' problems posed in [3, 4] we present here some results on one of them-namely on Cobweb Tiling Problem. Kwa´sniewski 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 σP k 1 ,k 2 ,...,ks of layer Φ 1 → Φ n. Then(More)
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 Kwa´sniewski general combinatorial(More)
This note is a response to one of the problems posed by Kwa´sniewski in [1, 2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic sequence F is at the point product of primary GCD-morphic sequences and any GCD-morphic sequence is encoded by natural number valued sequence satisfying condition (C1). The problem of general importance-for(More)
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 considered and(More)