Witt rings and matroids

Craven, Thomas; Kent, Zachary

doi:10.1090/S0002-9939-2012-11428-5

Witt rings and matroids
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by Thomas C. Craven and Zachary A. Kent

Proc. Amer. Math. Soc. 141 (2013), 1505-1517

DOI: https://doi.org/10.1090/S0002-9939-2012-11428-5

Published electronically: October 11, 2012

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Abstract:

The study of Witt rings of formally real fields in the algebraic theory of quadratic forms has led to a particularly good understanding of the finitely generated torsion free Witt rings. In this paper, we work primarily with a somewhat more general class of rings which can be completely characterized by (binary) matroids. The different types of standard constructions and invariants coming from algebra and from combinatorics lead to previously unstudied problems for both areas; in particular, there are new invariants for Witt rings and new constructions for matroids with many open questions.

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