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)
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)
In response to [6], 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)
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