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Weight-preserving bijections between integer partitions and a class of alternating sign trapezoids. (English) Zbl 1497.05015

Summary: 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.

MSC:

05A18 Partitions of sets
05A17 Combinatorial aspects of partitions of integers
15B35 Sign pattern matrices
05A15 Exact enumeration problems, generating functions
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05A19 Combinatorial identities, bijective combinatorics

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