X iv : m at h . C O / 0 21 12 85 v 2 3 O ct 2 00 3 Loops , matchings and alternating - sign matrices ∗
نویسنده
چکیده
The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes on matchings is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of alternating sign matrices and lozenge tilings of hexagons with cut off corners.
منابع مشابه
3 O ct 2 00 3 Loops , matchings and alternating - sign matrices ∗
The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes on matchings is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of alternating sign matrices and lozenge tilings of hexagons with cut off corners.
متن کاملar 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
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 t...
متن کاملar 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.
متن کاملar X iv : 0 80 3 . 26 97 v 1 [ m at h - ph ] 1 8 M ar 2 00 8 The limit shape of large alternating sign matrices
The problem of the limit shape of large alternating sign matrices (ASMs) is addressed by studying the emptiness formation probability (EFP) in the domain-wall six-vertex model. Assuming that the limit shape arises in correspondence to the 'condensation' of almost all solutions of the saddle-point equations for certain multiple integral representation for EFP, the limit shape of large ASMs is fo...
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تاریخ انتشار 2003