COMBINATORICS
2004
13 years 4 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, . . . ....
COMBINATORICS
2004
13 years 4 months ago
2004
New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures a...
COMBINATORICS
2004
13 years 4 months ago
2004
COMBINATORICS
2004
13 years 4 months ago
2004
COMBINATORICS
2004
13 years 4 months ago
2004
COMBINATORICS
2004
13 years 4 months ago
2004
Erdos posed the problem of how many random subsets need to be chosen from a set of n elements, each element appearing in each subset with probability p = 1/2, in order that at lea...
COMBINATORICS
2004
13 years 4 months ago
2004
We prove Borchardt's identity det 1 xi - yj per 1 xi - yj = det 1 (xi - yj)2 by means of sign-reversing involutions.
COMBINATORICS
2004
13 years 4 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
2004
13 years 4 months ago
2004
In the 1960's, Tutte presented a decomposition of a 2-connected finite graph into 3-connected graphs, cycles and bonds. This decomposition has been used to reduce problems on...
COMBINATORICS
2004
13 years 4 months ago
2004