Geodesic
A fourfold refined enumeration of alternating sign trapezoids
Hans Höngesberg1
1Universität Wien
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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Alternating sign trapezoids have recently been introduced as a generalisation of alternating sign triangles. Fischer established a threefold refined enumeration of alternating sign trapezoids and provided three statistics on column strict shifted plane partitions with the same joint distribution. In this paper, we are able to add a new pair of statistics to these results. More precisely, we consider the number of $-1$s on alternating sign trapezoids and introduce a corresponding statistic on column strict shifted plane partitions that has the same distribution. More generally, we show that the joint distributions of the two quadruples of statistics on alternating sign trapezoids and column strict shifted plane partitions, respectively, coincide. In addition, we provide a closed-form expression for the $2$-enumeration of alternating sign trapezoids.
DOI : 10.37236/9933
Classification : 05A15, 05A17, 15B35
Mots-clés : gog trapezoid, magog trapezoid, alternating sign matrix, plane partition

Hans Höngesberg  1

1 Universität Wien 
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     title = {A fourfold refined enumeration of alternating sign trapezoids},
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Hans Höngesberg. A fourfold refined enumeration of alternating sign trapezoids. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/9933

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