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The study investigates arithmetic properties of subsum polynomials related to partitions of n, suggesting connections to combinatorial objects.
We introduce the subsum polynomial of a partition λ =(λ ₁, λ ₂, … , λ ₖ) λ = ( λ 1 , λ 2 , … , λ k ) defined by sp(λ , x)=∏ ᵢ₌₁ᵏ(1+xλ ᵢ) sp ( λ , x ) = ∏ i = 1 k ( 1 + x λ i ) . We study the sum of reciprocals of sp(λ , 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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Ballantine et al. (2026) studied this question.
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