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COMBINATORICS
2006
153views more  COMBINATORICS 2006»
14 years 9 months ago
BG-Ranks and 2-Cores
We find the number of partitions of n whose BG-rank is j, in terms of pp(n), the number of pairs of partitions whose total number of cells is n, giving both bijective and generati...
William Y. C. Chen, Kathy Q. Ji, Herbert S. Wilf
COMBINATORICS
2006
116views more  COMBINATORICS 2006»
14 years 9 months ago
The Circular Chromatic Index of Flower Snarks
We determine the circular chromatic index of flower snarks, by showing that c(F3) = 7/2, c(F5) = 17/5 and c(Fk) = 10/3 for every odd integer k 7, where Fk denotes the flower snar...
Mohammad Ghebleh, Daniel Král, Serguei Nori...
COMBINATORICS
2006
108views more  COMBINATORICS 2006»
14 years 9 months ago
Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative ...
Nantel Bergeron, Christophe Hohlweg, Mercedes Rosa...
COMBINATORICS
2006
96views more  COMBINATORICS 2006»
14 years 9 months ago
A New Statistic on Linear and Circular r-Mino Arrangements
We introduce a new statistic on linear and circular r-mino arrangements which leads to interesting polynomial generalizations of the r-Fibonacci and r-Lucas sequences. By studying...
Mark A. Shattuck, Carl G. Wagner
COMBINATORICS
2006
140views more  COMBINATORICS 2006»
14 years 9 months ago
Characterization of [1, k]-Bar Visibility Trees
A unit bar-visibility graph is a graph whose vertices can be represented in the plane by disjoint horizontal unit-length bars such that two vertices are adjacent if and only if th...
Guantao Chen, Joan P. Hutchinson, Ken Keating, Jia...