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COMBINATORICS
2000
14 years 11 months ago
2000
We prove a conjecture of Cohn and Propp, which refines a conjecture of Bosley and Fidkowski about the symmetry of the set of alternating sign matrices (ASMs). We examine data aris...
COMBINATORICS
2000
14 years 11 months ago
2000
Let fr n(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12 . . . k, and let Fr(x; k) and F (x, y; k) be the generating functions d...
COMBINATORICS
2000
14 years 11 months ago
2000
Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Math...
COMBINATORICS
2000
14 years 11 months ago
2000
In a previous paper it was established that there are at least 27 non-isomorphic strongly regular (40, 12, 2, 4) graphs. Using a different and more efficient method we have re-inv...
COMBINATORICS
2000
14 years 11 months ago
2000
Given an integer n 2, and a non-negative integer k, consider all affine hyperplanes in Rn of the form xi = xj +r for i, j [n] and a non-negative integer r k. Let n,k be the pos...