How Many Subsets Which Their Operations With a Fixed Subset Contain at Least One Element of a Given Collection?
Year: 2024
Type: article
Abstract: We pose the following problem related to binary set operations on finite sets. Given a finite set . Let a binary set operation and be a non-empty collection of non-empty subsets of . For a fixed subset of , where , how many subsets of which their operation with contains at least one element of ?. In this paper, we give the solution of this problem, especially for the subsets of size , using the inclusion-exclusion principle, Corrádi’s lemma, and Bonferroni’s inequality. In this context, the problem is related to determining the degree of nodes in certain graphs, such as graphs constructed with the adjacency rule depends on and the node set is a hypergraph.
Authors: Muhammad Nurul Huda, Veni Rizki Lestari
Institution: Universitas Gadjah Mada
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403412518