Omega and Related Counting Polynomials

Abstract

Counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. In the present paper three related counting polynomials are discussed: Omega : , Equidistance 4 and Non-Equidistance 3 polynomials, and their mutual inter-relations in some particular graphs and lattices, as well. Analytical close formulas for some cubic lattices and their corresponding cages are derived.