M. Dziemiańczuk | Searcharxiv

arXiv2008

On GCD-morphic sequences

This note is a response to one of the problems posed by Kwaśniewski 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 example in number theory was formulated in [1,2] while investigating a new class of DAG's and their correspondent p.o. sets encoded uniquely by sequences with combinatorially interpretable properties.

math.CO↗

arXiv2008

On Cobweb Admissible Sequences - The Production Theorem

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 Dziemiańczuk) 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 admissible sequences taking values one and/or certain power of an appropriate primary number p. Here also an algorithm to produce the family of all cobweb-admissible sequences i.e. the Problem 1 from [1] i.e. one of several problems posed in source papers [2,3] is solved using the idea and methods implicitly present already in [4]

math.CO↗