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COMBINATORICS
2000
142views more  COMBINATORICS 2000»
13 years 5 months ago
Harmonic Functions on Multiplicative Graphs and Interpolation Polynomials
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...
Alexei Borodin, Grigori Olshanski
COMBINATORICS
2000
85views more  COMBINATORICS 2000»
13 years 5 months ago
Parity Systems and the Delta-Matroid Intersection Problem
We consider the problem of determining when two delta-matroids on the same ground-set have a common base. Our approach is to adapt the theory of matchings in 2-polymatroids develo...
André Bouchet, Bill Jackson
COMBINATORICS
2000
75views more  COMBINATORICS 2000»
13 years 5 months ago
Franklin's Argument Proves an Identity of Zagier
Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number...
Robin J. Chapman
COMBINATORICS
2000
87views more  COMBINATORICS 2000»
13 years 5 months ago
Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers
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...
Harold Fredricksen, Melvin M. Sweet
COMBINATORICS
2000
120views more  COMBINATORICS 2000»
13 years 5 months ago
The Characteristic Polynomial of a Graph is Reconstructible from the Characteristic Polynomials of its Vertex-Deleted Subgraphs
The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted subgraphs is one of the many...
Elias M. Hagos