On partitions with k corners not containing the staircase with one more corner

Description

We give three proofs of the following result conjectured by Carriegos, De Castro-Garc\'ıa and Muñoz Castañeda in their work on enumeration of control systems: when (k+12)≤n<(k+22), there are as many partitions of n with k corners as pairs of partitions (α,β) such that (k+12)+|α|+|β|=n.

Abstract

Ministerio de Economía y Competitividad MTM2016-75024-P

Abstract

Junta de Andalucía FQM333

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