JCT
2011
13 years 2 months ago
2011
JCT
2011
13 years 2 months ago
2011
We consider the problem of orienting the edges of the n-dimensional hypercube so only two different in-degrees a and b occur. We show that this can be done, for two specified in...
JCT
2011
13 years 2 months ago
2011
Abstract. Based on the ideas in [CKP], we introduce the weighted analogue of the branching rule for the classical hook length formula, and give two proofs of this result. The firs...
JCT
2011
13 years 2 months ago
2011
JCT
2011
13 years 2 months ago
2011
For a positive integer n that is not a power of 2, precisely the same family of convex polygons with n sides is optimal in three different geometric problems. These polygons have ...
JCT
2011
13 years 2 months ago
2011
JCT
2011
13 years 2 months ago
2011
We give combinatorial proofs of the formulas for the number of multichains in the k-divisible noncrossing partitions of classical types with certain conditions on the rank and the ...
JCT
2011
13 years 2 months ago
2011
JCT
2011
13 years 2 months ago
2011
The Baxter number Bn can be written as Bn = n k=0 Θk,n−k−1 with Θk,ℓ = 2 (k + 1)2 (k + 2) k + ℓ k k + ℓ + 1 k k + ℓ + 2 k . These numbers have first appeared in the...
JCT
2011
13 years 2 months ago
2011
We extend (and somewhat simplify) the algebraic proof technique of Guth and Katz [7], to obtain several sharp bounds on the number of incidences between lines and points in three ...