Counting on rectangular areas

TL;DR

This paper proves a theorem about the number of identical columns in a rectangular area and applies it to derive combinatorial identities by counting specific subsets.

Contribution

It introduces a new theorem for counting identical columns in rectangles and uses it to derive combinatorial identities.

Findings

Theorem for counting identical columns in rectangles.

Derivation of new combinatorial identities.

Application of the theorem to finite set subsets.

Abstract

In the first section of this paper we prove a theorem for the number of columns of a rectangular area that are identical to the given one. In the next section we apply this theorem to derive several combinatorial identities by counting specified subsets of a finite set.