On Cobweb Admissible Sequences - The Production Theorem

TL;DR

This paper discusses cobweb admissible sequences, providing a proof of a key theorem, and introduces an algorithm to generate all such sequences based on primary sequences and their prime power structures.

Contribution

It offers a proof of the Production Theorem for cobweb admissible sequences and presents an algorithm to produce all such sequences, solving an open problem.

Findings

Proof of the Production Theorem for cobweb admissible sequences

Algorithm for generating all cobweb admissible sequences

Characterization of sequences as products of primary sequences

Abstract

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 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]