M. Bousquet -- Melou and L. Habsieger, "Sur les matrices a signes alternants", Discrete Math. 139, 1995, 57 -- 72.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem of enumerating alternating sign matrices (ASMs) Alternating sign matrices are square n n matrices whose entries are either 0,1, such that the non zero elements in each row and column alternate between 1 and 1 and begin and end with 1. It is readily shown the there is a bijection[1] between alternating sign matrices (ASMs) and n certain osculating paths. An example of this bijection is illustrated in figure 2. The expression of RRM[2, 3] a n = n 1 i=1 (3i 1) n i) 1) for the number of nn ASMs was first impressively proved by Zeilberger [4] who related it to a ....

Mireille Bousquet-Melou Laurent Habsieger. Sur les matrices a signes alternants. Discrete Mathematics, 139:57--72, 1995.

....walkers may touch at a vertex, but then must part. The osculating walker model is an especially intriguing one, as it can be seen as a six vertex model, cf. 21] and because, with special boundary conditions, it produces famous objects in enumerative combinatorics, alternating sign matrices, cf. [4, 7]. Only numerical conjectures for exponents were obtained in [22] for the general n friendly walker model. Here we provide asymptotics for this model, which both prove the earlier conjectures, and makes the earlier results more precise. In this paper we first re derive the results of [21] by ....

M. Bousquet--M'elou and L. Habsieger, Sur les matrices `a signes alternants, Discrete Math. 139 (1995), 57--72.

....under a reflection about a vertical axis, it must obviously be of odd order 2n 1, since otherwise there would be a row containing two successive nonzero entries with the same sign. For the same reason, such a matrix cannot contain any 0 in its central column as seen in the example (4. 1) In [15], cf. also [16] Ch. 7.1, an equivalent counting problem via a bijection to families of disjoint paths in a square lattice is presented. Denote the vertices corresponding to the entry a ij in the ASM by (i, j) i, j =0, n 1. Then following the outermost path from (n 1, 0) to (0,n 1) the ....

M. Bousquet -- Melou and L. Habsieger, "Sur les matrices a signes alternants", Discrete Math. 139, 1995, 57 -- 72.

....touch at a vertex, but then must part, and so on. The osculating walker model is an especially intriguing one, as it can be seen as a six vertex model, cf. 21] and because, with special boundary conditions, it produces famous objects in enumerative combinatorics, alternating sign matrices, cf. [4, 7]. Walkers that may share an arbitrary number of steps we call the 1 friendly walker model. Only numerical conjectures for exponents were obtained in [22] for the general n friendly walker model. Here we provide asymptotics for this model, which both prove the earlier conjectures, and makes the ....

M. Bousquet--M'elou and L. Habsieger, Sur les matrices `a signes alternants, Discrete Math. 139 (1995), 57--72.

....problem of enumerating alternating sign matrices (ASMs) Alternating sign matrices are square n n matrices whose entries are either 0, 1, such that the non zero elements in each row and column alternate between 1 and 1 and begin and end with 1. It is readily shown the there is a bijection[1] between alternating sign matrices (ASMs) and n certain osculating paths. An example of this bijection is illustrated in figure 2. The expression of RRM[2, 3] a n = n 1 Y i=1 (3i 1) n i) 1) for the number of n n ASMs was first impressively proved by Zeilberger [4] who related it to a ....

Mireille Bousquet-Melou Laurent Habsieger. Sur les matrices a signes alternants. Discrete Mathematics, 139:57--72, 1995.

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M. Bousquet -- Melou and L. Habsieger, "Sur les matrices a signes alternants", Discrete Math. 139, 1995, 57 -- 72.

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