Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mutation classes of skew-symmetrizable $ 3\times3$ matrices


Author: Ahmet I. Seven
Journal: Proc. Amer. Math. Soc. 141 (2013), 1493-1504
MSC (2010): Primary 05E15; Secondary 15B36, 05C22, 13F60
Published electronically: September 27, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Mutation of skew-symmetrizable matrices is a fundamental operation that first arose in Fomin-Zelevinsky's theory of cluster algebras; it also appears naturally in many different areas of mathematics. In this paper, we study mutation classes of skew-symmetrizable $ 3\times 3$ matrices and associated graphs. We determine representatives for these classes using a natural minimality condition, generalizing and strengthening results of Beineke-Brustle-Hille and Felikson-Shapiro-Tumarkin. Furthermore, we obtain a new numerical invariant for the mutation operation on skew-symmetrizable matrices of arbitrary size.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05E15, 15B36, 05C22, 13F60

Retrieve articles in all journals with MSC (2010): 05E15, 15B36, 05C22, 13F60


Additional Information

Ahmet I. Seven
Affiliation: Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey
Email: aseven@metu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11477-7
PII: S 0002-9939(2012)11477-7
Received by editor(s): March 3, 2011
Received by editor(s) in revised form: August 17, 2011, and August 26, 2011
Published electronically: September 27, 2012
Additional Notes: The author’s research was supported in part by the Scientific and Technological Research Council of Turkey (TUBITAK), grant #110T207
Communicated by: Harm Derksen
Article copyright: © Copyright 2012 American Mathematical Society