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COMBINATORICS
2006
15 years 3 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...
167
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COMBINATORICS
2006
15 years 3 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...
143
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COMBINATORICS
2006
15 years 3 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...
138
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COMBINATORICS
2007
15 years 3 months ago
2007
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and finite di...
116
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COMBINATORICS
2007
15 years 3 months ago
2007
The known bijections on Dyck paths are either involutions or have notoriously intractable cycle structure. Here we present a size-preserving bijection on Dyck paths whose cycle st...