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COMBINATORICS
1998
14 years 9 months ago
1998
Based on a recent improvement of the inclusion-exclusion principle, we present a new approach to network reliability problems. In particular, we give a new proof of a result of Sh...
COMBINATORICS
1998
14 years 9 months ago
1998
New lower bounds for 15 classical Ramsey numbers are established. Several of the colorings are found using a new variation of local search heuristics. Several others are found usi...
COMBINATORICS
1998
14 years 9 months ago
1998
We prove that the minimal length of a word Sn having the property that it contains exactly Fm+2 distinct subwords of length m for 1 ≤ m ≤ n is Fn + Fn+2. Here Fn is the nth Fi...
COMBINATORICS
1999
14 years 9 months ago
1999
Let m and n be positive integers, and let R = (r1, . . . , rm) and S = (s1, . . . , sn) be non-negative integral vectors. Let A(R, S) be the set of all m
COMBINATORICS
1999
14 years 9 months ago
1999
We compute the number of rhombus tilings of a hexagon with sides n, n, N, n, n, N, where two triangles on the symmetry axis touching in one vertex are removed. The case of the comm...