Cyclotomic and simplicial matroids
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Issue Date
2005-12Author
Martin, Jeremy L.
Reiner, Victor
Publisher
Springer Verlag
Type
Article
Article Version
Scholarly/refereed, author accepted manuscript
Version
http://arxiv.org/abs/math.CO/0402206
Metadata
Show full item recordAbstract
We show that two naturally occurring matroids representable over ℚ are equal: thecyclotomic matroid µn represented by then th roots of unity 1, ζ, ζ2, …, ζn-1 inside the cyclotomic extension ℚ(ζ), and a direct sum of copies of a certain simplicial matroid, considered originally by Bolker in the context of transportation polytopes. A result of Adin leads to an upper bound for the number of ℚ-bases for ℚ(ζ) among then th roots of unity, which is tight if and only ifn has at most two odd prime factors. In addition, we study the Tutte polynomial of µn in the case that n has two prime factors.
Description
This is the author's accepted manuscript.
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Citation
Cyclotomic and simplicial matroids (with Victor Reiner), Israel Journal of Mathematics 150 (2005), 229--240.
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