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DENOMINATOR VECTORS AND COMPATIBILITY DEGREES IN CLUSTER ALGEBRAS OF FINITE TYPE.
- Source :
- Transactions of the American Mathematical Society; Feb2015, Vol. 367 Issue 2, p1421-1439, 19p
- Publication Year :
- 2015
-
Abstract
- We present two simple descriptions of the denominator vectors of the cluster variables of a cluster algebra of finite type, with respect to any initial cluster seed: one in terms of the compatibility degrees between almost positive roots defined by S. Fomin and A. Zelevinsky, and the other in terms of the root function of a certain subword complex. These descriptions only rely on linear algebra. They provide two simple proofs of the known fact that the d-vector of any non-initial cluster variable with respect to any initial cluster seed has non-negative entries and is different from zero. [ABSTRACT FROM AUTHOR]
- Subjects :
- VECTOR algebra
FINITE groups
CLUSTER algebras
MATHEMATICAL variables
POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 367
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 99639939
- Full Text :
- https://doi.org/10.1090/s0002-9947-2014-06239-9