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Cylindrical Dyck paths and the Mazorchuk–Turowska equation
- Source :
- Journal of Algebraic Combinatorics. 44:223-247
- Publication Year :
- 2016
- Publisher :
- Springer Science and Business Media LLC, 2016.
-
Abstract
- We classify all solutions (p,q) to the equation p(u)q(u)=p(u+b)q(u+a) where p and q are complex polynomials in one indeterminate u, and a and b are fixed but arbitrary complex numbers. This equation is a special case of a system of equations which ensures that certain algebras defined by generators and relations are non-trivial. We first give a necessary condition for the existence of non-trivial solutions to the equation. Then, under this condition, we use combinatorics of generalized Dyck paths to describe all solutions and a canonical way to factor each solution into a product of irreducible solutions.<br />21 pages
- Subjects :
- Algebra and Number Theory
010102 general mathematics
Mathematics - Rings and Algebras
System of linear equations
01 natural sciences
Combinatorics
Rings and Algebras (math.RA)
0103 physical sciences
FOS: Mathematics
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
Beta (velocity)
Combinatorics (math.CO)
010307 mathematical physics
0101 mathematics
Complex quadratic polynomial
Complex number
Mathematics
Subjects
Details
- ISSN :
- 15729192 and 09259899
- Volume :
- 44
- Database :
- OpenAIRE
- Journal :
- Journal of Algebraic Combinatorics
- Accession number :
- edsair.doi.dedup.....1b3f0ef310340a86b5d341bcc09f541a