منابع مشابه
Smith normal form and Laplacians
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.
متن کاملSmith normal form in combinatorics
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...
متن کاملThe Smith Normal Form of a Matrix
In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...
متن کاملThe Smith Normal Form of a Matrix
In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...
متن کاملOrthogonal 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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00163-2