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COMBINATORICS

2006

9 years 10 months ago
2006

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...

COMBINATORICS

2006

9 years 10 months ago
2006

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...

COMBINATORICS

2006

9 years 10 months ago
2006

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...

COMBINATORICS

2006

9 years 10 months ago
2006

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...

COMBINATORICS

2006

9 years 10 months ago
2006

We prove the Razumov

COMBINATORICS

2006

9 years 10 months ago
2006

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...

COMBINATORICS

2006

9 years 10 months ago
2006

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...

COMBINATORICS

2006

9 years 10 months ago
2006

We give a simpler proof of the result of Boros and F

COMBINATORICS

2006

9 years 10 months ago
2006

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...

COMBINATORICS

2006

9 years 10 months ago
2006

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...