JCT
2011
12 years 11 months ago
2011
JCT
2011
12 years 11 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
12 years 11 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
12 years 11 months ago
2011
JCT
2011
12 years 11 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
12 years 11 months ago
2011
JCT
2011
12 years 11 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
12 years 11 months ago
2011
JCT
2011
12 years 11 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
12 years 11 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 ...