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

Emmanuel Briand

doi:10.1016/j.dam.2022.02.012

paper

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

arXiv:2004.13180 · doi:10.1016/j.dam.2022.02.012

Abstract

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 $(2 k + 1) \leq n < (2 k + 2)$ , there are as many partitions of $n$ with $k$ corners as pairs of partitions $(α, β)$ such that $(2 k + 1) + ∣ α ∣ + ∣ β ∣ = n$ .

11 pages, 4 figures. Minor changes

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

Abstract

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