number-theory / Partitions and q-series
Ballantine, Beck, Feigon and Maurischat introduced the subsum polynomial $\mathrm{sp}(\lambda,x) := \prod_i (1+x^{\lambda_i})$ attached to an integer partition $\lambda$, studied rational functions built by summing reciprocals of these polynomials over natural classes of partitions, and posed ten conjectures. Six are now proved: the ordinary and binary coprimality and divisibility conjectures, and the odd and ternary special-value and recurrence conjectures.
Temporal state
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Append-only history
six of the ten conjectures proved; one was found false as printed and its corrected form remains open
Research memory
Ballantine, Beck, Feigon and Maurischat introduced the subsum polynomial $\mathrm{sp}(\lambda,x) := \prod_i (1+x^{\lambda_i})$ attached to an integer partition $\lambda$, studied rational functions built by summing reciprocals of these polynomials over natural classes of partitions, and posed ten conjectures. Six are now proved: the ordinary and binary coprimality and divisibility conjectures, and the odd and ternary special-value and recurrence conjectures.
six of the ten conjectures proved; one was found false as printed and its corrected form remains open
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