Forbidden subposet problems with size restrictions

TL;DR

This paper establishes upper bounds on the size of subset families avoiding specific inclusion-based configurations and size restrictions, advancing the understanding of forbidden subposet problems with additional constraints.

Contribution

It introduces new upper bounds for families avoiding certain inclusion patterns combined with size restrictions, extending classical forbidden subposet results.

Findings

Derived upper bounds for subset families avoiding specified configurations

Connected size-restricted problems to classical forbidden subposet problems

Enhanced understanding of inclusion pattern constraints in subset families

Abstract

Upper bounds to the size of a family of subsets of an n-element set that avoids certain configurations are proved. These forbidden configurations can be described by inclusion patterns and some sets having the same size. Our results are closely related to the forbidden subposet problems, where the avoided configurations are described solely by inclusions.