Alder-type partition inequality at the general level

초록

A known Alder-type partition inequality of level a , which involves the second Rogers- Ramanujan identity when the level a is 2, states that the number of partitions of n into parts differing by at least d with the smallest part being at least a is greater than or equal to that of partitions of n into parts congruent to +/- a ( mod d + 3 ) , excluding the part d + 3 - a . In this paper, we prove that for all values of d with a finite number of exceptions, an arbitrary level a Alder-type partition inequality holds without requiring the exclusion of the part d + 3 - a in the latter partition. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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