2–enumerations of Halved Alternating Sign Matrices
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چکیده
2–ENUMERATIONS OF HALVED ALTERNATING SIGN MATRICES THERESIA EISENKÖLBL Institut für Mathematik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria. E-mail: [email protected] Abstract. We compute 2–enumerations of certain halved alternating sign matrices. In one case the enumeration equals the number of perfect matchings of a halved Aztec diamond. In the other case the enumeration equals the number of perfect matchings of a halved fortress graph. Our results prove three conjectures by Jim Propp. An alternating sign matrix is a square matrix with entries 0, 1,−1 where the entries 1 and −1 alternate in each row and column and the sum of entries in each row and column is equal to 1. An example of an alternating sign matrix of order 6 is
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