Geodesic
Maximum exponent of Boolean circulant matrices with constant number of nonzero entries in their generating vector
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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It is well-known that the maximum exponent that an $n$-by-$n$ boolean primitive circulant matrix can attain is $n-1$. In this paper, we find the maximum exponent attained by $n$-by-$n$ boolean primitive circulant matrices with constant number of nonzero entries in their generating vector. We also give matrices attaining such exponents. Solving this problem we also solve two equivalent problems: 1) find the maximum exponent attained by primitive Cayley digraphs on a cyclic group whose vertices have constant outdegree; 2) determine the maximum order of a basis for ${\Bbb Z}_{n}$ with fixed cardinality.
DOI : 10.37236/155
Classification : 15B34, 05C25, 05C50
Mots-clés : Boolean primitive circulant matrix, primitive Cayley digraph 
@article{10_37236_155,
     author = {M. I. Bueno and S. Furtado and N. Sherer},
     title = {Maximum exponent of {Boolean} circulant matrices with constant number of nonzero entries in their generating vector},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/155},
     zbl = {1165.05329},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/155/}
}
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M. I. Bueno; S. Furtado; N. Sherer. Maximum exponent of Boolean circulant matrices with constant number of nonzero entries in their generating vector. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/155

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