Basics of the theory of cyclic rook polynomials and cyclic permanents of rectangular matrices

TL;DR

This paper introduces combinatorial formulas for cyclic rook polynomials and cyclic permanents of rectangular matrices, expanding understanding of their properties through row-based expansions.

Contribution

It provides new combinatorial formulas for cyclic rook polynomials and cyclic permanents specifically for rectangular matrices, enhancing theoretical understanding.

Findings

Derived combinatorial formulas for cyclic rook polynomials.

Presented expansions of cyclic permanents along rows.

Enhanced theoretical framework for matrix combinatorics.

Abstract

Combinatorial formulas expressing cyclic rook polynomials and cyclic permanents of rectangular matrices in terms of expansions along rows are presented