ScholarWorks@숙명여자대학교

초록

We insert additional variables into Warnaar's q-analogue of Nicomachus' identity and other related identities, and compute discriminants with respect to q. Factorization of these discriminants reveals pairs of partitions that conjecturally relate in the manner of Wheatstone. The factorization also yields, conjecturally, families of polynomials with relations to various Molien series, remarkable rational generating functions, and notable root distributions. For a q-analogue of Nicomachus' identity produced by Cigler, we provide proofs of the partition properties. We also state and in part prove tight inequalities for the elements of two interlacing sequences that led us to the "twin" of Warnaar's q-analogue.

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