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102
Voted
COMBINATORICS
2004
15 years 3 months ago
2004
For any integer r 2, define a sequence of numbers {c (r) k }k=0,1,..., independent of the parameter n, by n k=0 n k r n + k k r = n k=0 n k n + k k c (r) k , n = 0, 1, 2, . . . ....
107
Voted
COMBINATORICS
2000
15 years 3 months ago
2000
It is shown in this note that with high probability it is enough to destroy all triangles in order to get a cover graph from a random graph Gn,p with p log n/n for any constant ...
119
Voted
COMBINATORICS
2000
15 years 3 months ago
2000
Let An denote the number of objects of some type of "size" n, and let Cn denote the number of these objects which are connected. It is often the case that there is a rel...
104
Voted
COMBINATORICS
2000
15 years 3 months ago
2000
Abstract. We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the q-Eulerian identities of Brenti and some generalizations. In particul...
127
Voted
COMBINATORICS
2000
15 years 3 months ago
2000
Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning...