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COMBINATORICS
2002
13 years 7 months ago
2002
If we compose sufficiently many random functions on a finite set, then the composite function will be constant. We determine the number of compositions that are needed, on average...
COMBINATORICS
2002
13 years 7 months ago
2002
We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm,...
COMBINATORICS
2002
13 years 7 months ago
2002
We present a new expression for the partition function of the dimer arrangements and the Ising partition function of the 3-dimensional cubic lattice. We use the Pfaffian method. T...
COMBINATORICS
2002
13 years 7 months ago
2002
A sequence u = u1u2...un is said to be nonrepetitive if no two adjacent blocks of u are exactly the same. For instance, the sequence abcbcba contains a repetition bcbc, while abca...
COMBINATORICS
2002
13 years 7 months ago
2002
We consider permutations that avoid the pattern 1324. By studying the generating tree for such permutations, we obtain a recurrence formula for their number. A computer program pr...