Factorizations and representations of binary polynomial recurrences by matrix methods
نویسندگان
چکیده
منابع مشابه
Factorizations and Representations of Binary Polynomial Recurrences by Matrix Methods
In this paper we derive factorizations and representations of a polynomial analogue of an arbitrary binary sequence by matrix methods. It generalizes various results on Fibonacci, Lucas, Chebyshev and MorganVoyce polynomials. 1. Introduction In [10], the divisibility properties of the Fibonacci polynomial sequence ffn (x)g was studied. The Fibonacci polynomial sequence is de ned by the recursi...
متن کاملFactorizations and representations of the backward second-order linear recurrences
We show the relationships between the determinants and permanents of certain tridiagonal matrices and the negatively subscripted terms of second-order linear recurrences.Also considering how to the negatively subscripted terms of second-order linear recurrences can be connected to Chebyshev polynomials by determinants of these matrices, we give factorizations and representations of these number...
متن کاملMatrix Factorizations and Representations of Quivers I
This paper introduces a mathematical definition of the category of D-branes in Landau-Ginzburg orbifolds in terms of A∞-categories. Our categories coincide with the categories of (gradable) matrix factorizations for quasi-homogeneous polynomials. After setting up the necessary definitions, we prove that our category for the polynomial x is equivalent to the derived category of representations o...
متن کاملNotes on n-D Polynomial Matrix Factorizations
This paper discusses a relationship between the prime factorizability of a normal full rank n-D (n > 2) polynomial matrix and its reduced minors. Two conjectures regarding the n-D polynomial matrix prime factorization problem are posed, and a partial solution to one of the conjectures is provided. Another related open problem of factorizing an n-D polynomial matrix that is not of normal full ra...
متن کاملMatrix Factorizations and Representations of Quivers Ii : Type Ade Case
We study a triangulated category of graded matrix factorizations for a polynomial of type ADE. We show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding Dynkin quiver. Also, we discuss a special stability condition for the triangulated category in the sense of T. Bridgeland, which is naturally defined by the grading.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2011
ISSN: 0035-7596
DOI: 10.1216/rmj-2011-41-4-1247