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DM
2008
13 years 10 months ago
2008
Catalan numbers C(n) = 1 n+1 2n n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n-...
CORR
2007
Springer
13 years 10 months ago
2007
Springer
—For a linear block code C, its stopping redundancy is defined as the smallest number of check nodes in a Tanner graph for C, such that there exist no stopping sets of size smal...
JCT
2007
13 years 10 months ago
2007
Given a sequence of integers b = (b0,b1,b2,...) one gives a Dyck path P of length 2n the weight wt(P) = bh1 bh2 ···bhn , where hi is the height of the ith ascent of P. The corr...
AI
1998
Springer
13 years 10 months ago
1998
Springer
Given a set of numbers, the two-way partitioning problem is to divide them into two subsets, so that the sum of the numbers in each subset are as nearly equal as possible. The pro...
JGT
2010
13 years 8 months ago
2010
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chv´atal, Newborn, Sze...