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COMBINATORICS
2006
113views more  COMBINATORICS 2006»
14 years 9 months ago
Tilings of the Sphere with Right Triangles II: The (1, 3, 2), (0, 2, n) Subfamily
Sommerville [8] and Davies [2] classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile t...
Robert J. MacG. Dawson, Blair Doyle
COMBINATORICS
2006
100views more  COMBINATORICS 2006»
14 years 9 months ago
Grid Classes and the Fibonacci Dichotomy for Restricted Permutations
We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof...
Sophie Huczynska, Vincent Vatter
COMBINATORICS
2006
109views more  COMBINATORICS 2006»
14 years 9 months ago
The Strongly Regular (45, 12, 3, 3) Graphs
Using two backtrack algorithms based on different techniques, designed and implemented independently, we were able to determine up to isomorphism all strongly regular graphs with ...
Kris Coolsaet, Jan Degraer, Edward Spence
COMBINATORICS
2006
88views more  COMBINATORICS 2006»
14 years 9 months ago
Tilings of the Sphere with Right Triangles I: The Asymptotically Right Families
Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile ...
Robert J. MacG. Dawson, Blair Doyle
COMBINATORICS
2006
153views more  COMBINATORICS 2006»
14 years 9 months ago
The Absence of Efficient Dual Pairs of Spanning Trees in Planar Graphs
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T in the dual graph G such that T and T do not intersect. We show that it is not always poss...
T. R. Riley, William P. Thurston