Linked partition ideals and Andrews-Gordon type series for Alladi and Gordon’s extension of Schur’s identity. (English) Zbl 1506.05019

Chern, Shane

Rocky Mt. J. Math. 52, No. 6, 2009-2026 (2022).

Summary: Based on the framework of linked partition ideals, we derive some double and triple series of Andrews-Gordon type for partitions in Alladi and Gordon’s extension of Schur’s identity. We also display similar series for such partitions with additional restrictions on the smallest part. Also, an alternative proof of Alladi and Gordon’s extension of Schur’s identity is presented.

MSC:

05A17	Combinatorial aspects of partitions of integers
05A15	Exact enumeration problems, generating functions
11P84	Partition identities; identities of Rogers-Ramanujan type

Keywords:

linked partition ideals; Andrews-Gordon-type series; Schur identity; generating function

References:

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