On finding a particular class of combinatorial identities
Krassimir Yankov Iordjev, Dimiter Stoichkov Kovachev
TL;DR
This paper introduces a new class of combinatorial identities proved using the classic counting in two ways method and the principle of inclusion-exclusion to derive properties of (0,1)-matrices.
Contribution
It presents a novel class of combinatorial identities and a method based on counting in two ways combined with inclusion-exclusion for analyzing (0,1)-matrices.
Findings
Established a new class of combinatorial identities.
Applied the counting in two ways method to derive identities.
Utilized inclusion-exclusion to analyze (0,1)-matrices.
Abstract
In this paper, a class of combinatorial identities is proved. A method is used which is based on the following rule: counting elements of a given set in two ways and making equal the obtained results. This rule is known as "counting in two ways". The principle of inclusion and exclusion is used for obtaining a class of (0,1)-matrices.
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Taxonomy
Topicsgraph theory and CDMA systems · Optics and Image Analysis · Graph Labeling and Dimension Problems