Orthogonal polynomials and Smith normal form
نویسندگان
چکیده
منابع مشابه
Orthogonal Polynomials and Smith Normal Form
Smith normal form evaluations found by Bessenrodt and Stanley for some Hankel matrices of q-Catalan numbers are proven in two ways. One argument generalizes the Bessenrodt–Stanley results for the Smith normal form of a certain multivariate matrix that refines one studied by Berlekamp, Carlitz, Roselle, and Scoville. The second argument, which uses orthogonal polynomials, generalizes to a number...
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Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ(G), obtained from the Smith normal form of M , and whose order is the number of spanning trees of G. We provide some general results on the relationship between the eigenvalues of M and the structure of Φ(G), and address the question of how often the group Φ(G) is cyclic.
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This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith normal form of random integer matrices. We then give some examples of Smith normal form and diagonal form arising from (1) symmetric functions, (2) a result of Ca...
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The Hermitian Lanczos method for Hermitian matrices has a wellknown connection with a 3-term recurrence for polynomials orthogonal on a discrete subset of R. This connection disappears for normal matrices with the Arnoldi method. In this paper we consider an iterative method that is more faithful to the normality than the Arnoldi iteration. The approach is based on enlarging the set of polynomi...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2017
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-017-1082-6