gog triangle | strict Gelfand pattern

A monotone triangle (also called a strict Gelfand pattern or a gog triangle) of order n is a number triangle with n numbers along each side and the base containing entries between 1 and n 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 n and alternating sign matrices of order n obtained by letting the kth row of the triangle equal the positions of 1s in the sum of the first k rows of an alternating sign matrix, as illustrated below.