Witt rings and matroids

Authors:
Thomas C. Craven and Zachary A. Kent

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

MSC (2010):
Primary 13M05; Secondary 12D15, 11E81

Published electronically:
October 11, 2012

MathSciNet review:
3020838

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Thomas C. Craven**

Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822

Email:
tom@math.hawaii.edu

**Zachary A. Kent**

Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322

Email:
kent@mathcs.emory.edu

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

Received by editor(s):
August 29, 2011

Published electronically:
October 11, 2012

Communicated by:
Ken Ono

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.