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COMBINATORICS
2004
112views more  COMBINATORICS 2004»
8 years 6 months ago
On a Combinatorial Problem of Asmus Schmidt
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, . . . ....
W. Zudilin
COMBINATORICS
2004
103views more  COMBINATORICS 2004»
8 years 6 months ago
On the Counting of Fully Packed Loop Configurations: Some New Conjectures
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...
Jean-Bernard Zuber
COMBINATORICS
2004
103views more  COMBINATORICS 2004»
8 years 6 months ago
Constructive Lower Bounds on Classical Multicolor Ramsey Numbers
Xu Xiaodong, Xie Zheng, Geoffrey Exoo, Stanislaw P...
COMBINATORICS
2004
93views more  COMBINATORICS 2004»
8 years 6 months ago
Classification of Six-Point Metrics
Bernd Sturmfels, Josephine Yu
COMBINATORICS
2004
69views more  COMBINATORICS 2004»
8 years 6 months ago
Convergence in Distribution for Subset Counts Between Random Sets
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...
Dudley Stark
COMBINATORICS
2004
112views more  COMBINATORICS 2004»
8 years 6 months ago
A Bijective Proof of Borchardt's Identity
We prove Borchardt's identity det 1 xi - yj per 1 xi - yj = det 1 (xi - yj)2 by means of sign-reversing involutions.
Dan Singer
COMBINATORICS
2004
94views more  COMBINATORICS 2004»
8 years 6 months ago
Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy
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...
James A. Sellers, Andrew V. Sills, Gary L. Mullen
COMBINATORICS
2004
82views more  COMBINATORICS 2004»
8 years 6 months ago
Decomposing Infinite 2-Connected Graphs into 3-Connected Components
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...
R. Bruce Richter
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