ar X iv : m at h . C O / 0 20 81 25 v 1 1 5 A ug 2 00 2 The many faces of alternating - sign matrices
نویسنده
چکیده
I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, threecolorings, monotone triangles, tetrahedral order ideals, square ice, gasketand-basket tilings and full packings of loops. (This article has been published in a conference edition of the journal Discrete Mathematics and Theoretical Computer Science, entitled “Discrete Models: Combinatorics, Computation, and Geometry,” edited by R. Cori, J. Mazoyer, M. Morvan, and R. Mosseri, and published in July 2001 in cooperation with le Maison de l’Informatique et des Mathématiques Discrètes, Paris, France: ISSN 13658050, http://dmtcs.lori.fr.)
منابع مشابه
ar X iv : m at h - ph / 0 40 40 45 v 2 2 5 N ov 2 00 4 On the refined 3 - enumeration of alternating sign matrices
An explicit expression for the numbers A(n, r; 3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n, r; 3)'s are represented as 1-fold sums which can also be written in terms of terminating 4 F 3 series of argument 1/4.
متن کاملar X iv : m at h - ph / 0 40 40 45 v 1 1 9 A pr 2 00 4 On the refined 3 - enumeration of alternating sign matrices
An explicit expression for the numbers A(n, r; 3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n, r; 3)'s are represented as 1-fold sums which can also be written in terms of terminating 4 F 3 series of argument 1/4.
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