Cyclotomic and simplicial matroids |
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Authors: | Jeremy L Martin Victor Reiner |
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Institution: | (1) School of Mathematics, University of Minnesota, 55455 Minneapolis, MN, USA |
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Abstract: | 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 thatn has two prime factors.
First author supported by NSF Postdoctoral Fellowship. Second author supported by NSF grant DMS-0245379. |
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