Monotone Triangle

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.

(1)

			(2)
			(3)
			(4)
			(5)
			(6)

REFERENCES:

Bressoud, D. and Propp, J. "How the Alternating Sign Matrix Conjecture was Solved." Not. Amer. Math. Soc. 46, 637-646.