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» On the combinatorics of Galois numbers
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COMBINATORICS
2006
126views more  COMBINATORICS 2006»
14 years 12 months ago
Bounding the Number of Edges in Permutation Graphs
Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and th...
Peter Keevash, Po-Shen Loh, Benny Sudakov
COMBINATORICS
2007
69views more  COMBINATORICS 2007»
14 years 12 months ago
On the Number of Genus One Labeled Circle Trees
A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-...
Karola Mészáros
COMBINATORICS
2004
103views more  COMBINATORICS 2004»
14 years 11 months ago
On the Counting of Fully Packed Loop Configurations: Some New Conjectures
New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures a...
Jean-Bernard Zuber
COMBINATORICS
2000
75views more  COMBINATORICS 2000»
14 years 11 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
120views more  COMBINATORICS 2000»
14 years 11 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