Alternating Sign Matrices and Descending Plane Partitions
Alternating Sign Matrices and Descending Plane Partitions
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交替符号矩阵和下降平面划分
DOI：
10.1016/0097-3165(83)90068-7
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
H. Rumsey
中科院分区：
文献类型：
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作者：
W. Mills;D. P. Robbins;H. Rumsey
交错符号矩阵是一个方阵，使得(I)所有项都是1、−1或0，(Ii)每行和列都有和1，以及(Iii)在每行和列中非零项的符号交替。这些矩阵与由Andrews(发明)引入的下降平面划分之间的联系的引人注目的数字证据。53(1979)，193-225)已被发现，但试图证明这种联系的存在没有成功。然而，这一证据确实提出了一种证明关于下降平面划分的安德鲁斯猜想的方法，这反过来又提出了一种证明关于循环对称平面划分的麦克唐纳猜想的方法(发明。数学66(1982)，73-87)。本文讨论了交错符号矩阵和降维平面划分，给出了关于它们的几个猜想和定理。
Analternating sign matrixis a square matrix such that (i) all entries are 1, −1, or 0, (ii) every row and column has sum 1, and (iii) in every row and column the nonzero entries alternate in sign. Striking numerical evidence of a connection between these matrices and the descending plane partitions introduced by Andrews (Invent. Math.53(1979), 193–225) have been discovered, but attempts to prove the existence of such a connection have been unsuccessful. This evidence, however, did suggest a method of proving the Andrews conjecture on descending plane partitions, which in turn suggested a method of proving the Macdonald conjecture on cyclically symmetric plane partitions (Invent. Math.66(1982), 73–87). In this paper is a discussion of alternating sign matrices and descending plane partitions, and several conjectures and theorems about them are presented.