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Loops, matchings and alternating-sign matrices. (English) Zbl 1070.05008

Summary: 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.

MSC:

05A15 Exact enumeration problems, generating functions
15B36 Matrices of integers

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