Cobweb posets as noncommutative prefabs

TL;DR

This paper introduces cobweb posets, a new class of infinite graded posets that serve as noncommutative prefab combinatorial schemas, expanding the framework by relaxing traditional algebraic constraints.

Contribution

It defines cobweb posets as noncommutative prefabs and explores their basic properties, broadening the scope of combinatorial schema construction.

Findings

Cobweb posets form a new class of infinite graded posets.

They provide noncommutative prefab combinatorial schemas.

Basic properties of cobweb prefabs are established.

Abstract

A class of new type graded infinite posets with minimal element are considered. These so called cobweb posets introduced recently by the present author provide a wide range of new noncommutative prefab combinatorial schema with characteristic graded subposets as primes. The schema are defined here via relaxing commutativity and associativity requirements imposed on the composition of prefabs by the fathers of this fertile concept. The construction and the very first basic properties of cobweb prefabs are pointed out in what follows. An another single valued commutative amd associative composision is also considered.