منابع مشابه
The Alternating Sign Matrix Polytope
The Birkhoff (permutation) polytope, Bn, consists of the n × n nonnegative doubly stochastic matrices, has dimension (n− 1)2, and has n2 facets. A new analogue, the alternating sign matrix polytope, ASMn, is introduced and characterized. Its vertices are the Qn−1 j=0 (3j+1)! (n+j)! n × n alternating sign matrices. It has dimension (n− 1)2, has 4[(n− 2)2 +1] facets, and has a simple inequality d...
متن کاملProof of the alternating sign matrix conjecture
Gert Almkvist, Noga Alon, George Andrews, Anonymous, Dror Bar-Natan, Francois Bergeron, Nantel Bergeron, Gaurav Bhatnagar, Anders Björner, Jonathan Borwein, Mireille Bousquest-Mélou, Francesco Brenti, E. Rodney Canfield, William Chen, Chu Wenchang, Shaun Cooper, Kequan Ding, Charles Dunkl, Richard Ehrenborg, Leon Ehrenpreis, Shalosh B. Ekhad, Kimmo Eriksson, Dominique Foata, Omar Foda, Aviezri ...
متن کاملProof of the Refined Alternating Sign Matrix Conjecture
Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order n equals A(n) := 1!4!7! · · · (3n − 2)! n!(n + 1)! · · · (2n − 1)! . Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) ‘1’ of the first row is at the rth column equals A(n) `n+r−2 n−1 ́`2n−1−r n−1 ́ `3n−2 n−1 ́ . Standing on...
متن کاملAnother Proof of the Alternating-Sign Matrix Conjecture
Alternating sign matrices are related to a number of other combinatorial objects that, remarkably, are also enumerated or conjectured to be enumerated by ratios of progressions of factorials or staggered factorials [9], [11]. Zeilberger [13] recently proved Theorem 1 by establishing that ASMs are equinumerous with totally symmetric, self-complementary plane partitions, which were enumerated by ...
متن کاملA new proof of the refined alternating sign matrix theorem
Abstract. In the early 1980s, Mills, Robbins and Rumsey conjectured, and in 1996 Zeilberger proved a simple product formula for the number of n × n alternating sign matrices with a 1 at the top of the i-th column. We give an alternative proof of this formula using our operator formula for the number of monotone triangles with prescribed bottom row. In addition, we provide the enumeration of cer...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/130