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COMBINATORICS
2004
13 years 9 months ago
2004
Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
COMBINATORICS
2004
13 years 9 months ago
2004
The Sandwich Theorems proved in this paper give a new method to show that the partition function a(n) of a partition identity A(x) := n=0 a(n)xn = n=1 (1 - xn )-p(n) satisfies t...
COMBINATORICS
2002
13 years 9 months ago
2002
An efficient and purely combinatorial algorithm for calculating products in arbitrary Coxeter groups is presented, which combines ideas of Fokko du Cloux and myself. Proofs are lar...
COMBINATORICS
2004
13 years 9 months ago
2004
We study the distribution of the statistics `number of fixed points' and `number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all th...
COMBINATORICS
2004
13 years 9 months ago
2004
It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at l...