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COMBINATORICS
2000
13 years 9 months ago
2000
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on th...
COMBINATORICS
2000
13 years 9 months ago
2000
We give new lower bounds for the Schur numbers S(6) and S(7). This will imply new lower bounds for the Multicolor Ramsey Numbers R6(3) and R7(3). We also make several observations...
COMBINATORICS
2000
13 years 9 months ago
2000
Bound polysemy is the property of any pair (G1, G2) of graphs on a shared vertex set V for which there exists a partial order on V such that any pair of vertices has an upper boun...
COMBINATORICS
2000
13 years 9 months ago
2000
: We prove two extensions of the Hales-Jewett coloring theorem. The first is a polynomial version of a finitary case of Furstenberg and Katznelson's multiparameter elaboration...
COMBINATORICS
2000
13 years 9 months ago
2000
A (multi)hypergraph H with vertices in N contains a permutation p = a1a2 . . . ak of 1, 2, . . . , k if one can reduce H by omitting vertices from the edges so that the resulting ...