Titel
A Fourfold Refined Enumeration of Alternating Sign Trapezoids
Abstract
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 −1s 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.
Stichwort
Computational Theory and MathematicsGeometry and TopologyTheoretical Computer ScienceApplied MathematicsDiscrete Mathematics and Combinatorics
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:1675002
Erschienen in
Titel
The Electronic Journal of Combinatorics
Band
29
Ausgabe
3
ISSN
1077-8926
Erscheinungsdatum
2022
Verlag
The Electronic Journal of Combinatorics
Erscheinungsdatum
2022
Zugänglichkeit
Rechteangabe
© The author

Herunterladen

Universität Wien | Universitätsring 1 | 1010 Wien | T +43-1-4277-0