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This research aims to analyze the reciprocals of subsum polynomials for different partitions, uncovering their algebraic relationships.

June 17, 2026Open Access

Reciprocals of subsum polynomials

Key Points

This research aims to analyze the reciprocals of subsum polynomials for different partitions, uncovering their algebraic relationships.
Introduced the subsum polynomial defined by a product of terms involving partitions.
Studied the sum of reciprocals of subsum polynomials over all partitions of a given integer n.
Proved various arithmetic properties of these polynomials and related them to combinatorial constructs.
Demonstrated new algebraic identities related to the sum of reciprocals of subsum polynomials.
Established connections between subsum polynomials and other known combinatorial objects in literature.

Abstract

Abstract We introduce the subsum polynomial of a partition = (₁, ₂, , ₖ) λ = (λ 1, λ 2, …, λ k) defined by sp (, x) = ₈=₁ᵏ (1+x^ ᵢ) sp (λ, x) = ∏ i = 1 k (1 + x λ i). We study the sum of reciprocals of sp (, x) sp (λ, x) over all partitions of n. We prove arithmetic properties of related polynomials and offer connections to other combinatorial objects.

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