Höngesberg, Hans A fourfold refined enumeration of alternating sign trapezoids. (English) Zbl 1496.05005 Electron. J. Comb. 29, No. 3, Research Paper P3.42, 27 p. (2022). Summary: Alternating sign trapezoids have recently been introduced as a generalisation of alternating sign triangles. I. Fischer [J. Comb. Theory, Ser. A 158, 560–604 (2018; Zbl 1391.05040)] 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. MSC: 05A15 Exact enumeration problems, generating functions 05A17 Combinatorial aspects of partitions of integers 15B35 Sign pattern matrices Keywords:gog trapezoid; magog trapezoid; alternating sign matrix; plane partition Citations:Zbl 1391.05040 PDFBibTeX XMLCite \textit{H. Höngesberg}, Electron. J. Comb. 29, No. 3, Research Paper P3.42, 27 p. (2022; Zbl 1496.05005) Full Text: DOI References: [1] George E. Andrews, Richard Askey, and Ranjan Roy.Special Functions. Encyclopedia of Mathematics and its Applications 71. 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