3 papers
math.CO2026
A proof of the Auluck-Chowla-Gupta Conjecture
Jaideep Sai Padhi
Let p(n,k) denote the number of partitions of n into exactly k parts. In 1942 Auluck, Chowla and Gupta conjectured that for every n the sequence p(n,1), p(n,2), ..., p(n,n) is unim…
math.CO2026
Sign patterns of real powers of infinite products: resolution of four conjectures of Schlosser and Zhou
Jaideep Sai Padhi
For an infinite product P(q) = prod_{m>=1} (1-q^m)^{eps(m)} and real delta, write P(q)^delta = sum_{n>=0} c_delta(n) q^n. Schlosser and Zhou conjectured precise sign patterns for t…
math.CO2026
Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics, with an Account of the Human-Machine Methodology Employed
Jaideep Sai Padhi
We report solutions to five challenge problems posed by Doron Zeilberger and his collaborators, together with substantial partial progress on two further problems, and we describe…