A monotone triangle (also called a strict Gelfand pattern or a gog triangle) of order is a number triangle with numbers along each side and the base containing entries between 1 and such that there is strict increase across rows and weak increase diagonally up or down to the right. There is a bijection between monotone triangles of order and alternating sign matrices of order obtained by letting the th row of the triangle equal the positions of 1s in the sum of the first rows of an alternating sign matrix, as illustrated below.
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