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SUMMARY 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 ([6,7] and references therein to the first author).[7,6,8] include natural enquires to be… (More)

- M. Dziemianczuk
- 2007

SUMMARY Kwa´sniewski'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… (More)

In this note further clue decisive observations on cobweb admissible sequences are shared with the audience. In particular an announced proof of the Theorem 1 (by Dziemia´nczuk) from [1] announced in India-Kolkata-December 2007 is delivered here. Namely here and there we claim that any cobweb admissible sequence F is at the point product of primary cobweb… (More)

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)

- M. Dziemianczuk
- 2008

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)

One considers here orderable acyclic digraphs named KoDAGs which represent the outmost general chains of di-bi-cliques denoting thus the outmost general chains of binary relations. Because of this fact KoDAGs start to become an outstanding concept of nowadays investigation. We propose here examples of codings of KoDAGs looked upon as infinite hyper-boxes as… (More)