Weight-preserving bijections between integer partitions and a class of alternating sign trapezoids

Abstract

We construct weight-preserving bijections between column strict shifted plane partitions with one row and alternating sign trapezoids with exactly one column in the left half that sums to $1$. Amongst other things, they relate the number of $-1$s in the alternating sign trapezoids to certain elements in the column strict shifted plane partitions that generalise the notion of special parts in descending plane partitions. The advantage of these bijections is that they include configurations with $-1$s, which is a feature that many of the bijections in the realm of alternating sign arrays lack.

18 pages, 12 figures. Final revised version to appear in Annals of Combinatorics

References in corpus (5)

• Back stable Schubert calculus
• Diagonally and antidiagonally symmetric alternating sign matrices of odd order
• Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
• A simple explicit bijection between (n,2) Gog and Magog trapezoids
• A Fourfold Refined Enumeration of Alternating Sign Trapezoids