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COMBINATORICS
2004
14 years 9 months ago
2004
In 1958, Richard Guy proved that the number of partitions of n into odd parts greater than one equals the number of partitions of n into distinct parts with no powers of 2 allowed...
COMBINATORICS
2000
14 years 9 months ago
2000
Let n be the fraction of structures of size" n which are connected"; e.g., a the fraction of labeled or unlabeled n-vertex graphshavingone component, b the fraction of p...
COMBINATORICS
2000
14 years 9 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 9 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...
COMBINATORICS
2000
14 years 9 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...