The number of monotone triangles with prescribed bottom row
classification
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keywords
bottommonotonetrianglesnumberprescribedalternatingbijectionformula
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We show that the number of monotone triangles with prescribed bottom row (k_1,...,k_n) is given by a simple product formula which remarkably involves (shift) operators. Monotone triangles with bottom row (1,2,...,n) are in bijection with $n \times n$ alternating sign matrices.
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