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COMBINATORICS
2006
121views more  COMBINATORICS 2006»
8 years 6 months ago
Asymptotics for Incidence Matrix Classes
We define incidence matrices to be zero-one matrices with no zero rows or columns. We are interested in counting incidence matrices with a given number of ones, irrespective of th...
Peter J. Cameron, Thomas Prellberg, Dudley Stark
COMBINATORICS
2006
169views more  COMBINATORICS 2006»
8 years 6 months ago
The Diameter and Laplacian Eigenvalues of Directed Graphs
For undirected graphs it has been known for some time that one can bound the diameter using the eigenvalues. In this note we give a similar result for the diameter of strongly con...
Fan R. K. Chung
COMBINATORICS
2006
144views more  COMBINATORICS 2006»
8 years 6 months ago
On an Identity for the Cycle Indices of Rooted Tree Automorphism Groups
This note deals with a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric grou...
Stephan G. Wagner
COMBINATORICS
2006
137views more  COMBINATORICS 2006»
8 years 6 months ago
Three-Letter-Pattern-Avoiding Permutations and Functional Equations
We present an algorithm for finding a system of recurrence relations for the number of permutations of length n that satisfy a certain set of conditions. A rewriting of these rela...
Ghassan Firro, Toufik Mansour
COMBINATORICS
2006
107views more  COMBINATORICS 2006»
8 years 6 months ago
On the Symmetry of the Distribution of k-Crossings and k-Nestings in Graphs
This note contains two results on the distribution of k-crossings and k-nestings in graphs. On the positive side, we exhibit a class of graphs for which there are as many k-noncro...
Anna de Mier
COMBINATORICS
2006
135views more  COMBINATORICS 2006»
8 years 6 months ago
Lyndon Words and Transition Matrices between Elementary, Homogeneous and Monomial Symmetric Functions
Let h, e, and m denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition respectively. We gi...
Andrius Kulikauskas, Jeffrey B. Remmel
COMBINATORICS
2006
125views more  COMBINATORICS 2006»
8 years 6 months ago
A Point in Many Triangles
We give a simpler proof of the result of Boros and F
Boris Bukh
COMBINATORICS
2006
142views more  COMBINATORICS 2006»
8 years 6 months ago
The Zeta Function of a Hypergraph
We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factor...
Christopher K. Storm
COMBINATORICS
2006
87views more  COMBINATORICS 2006»
8 years 6 months ago
Optimal Four-Dimensional Codes over GF(8)
We prove the nonexistence of several four-dimensional codes over GF(8) that meet the Griesmer bound. The proofs use geometric methods based on the analysis of the weight structure...
Chris Jones, Angela Matney, Harold N. Ward
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