Smith normal form of a multivariate matrix associated with partitions
نویسندگان
چکیده
منابع مشابه
Smith Normal Form of a Multivariate Matrix Associated with Partitions
Abstract. Considering a question of E. R. Berlekamp, Carlitz, Roselle, and Scoville gave a combinatorial interpretation of the entries of certain matrices of determinant 1 in terms of lattice paths. Here we generalize this result by refining the matrix entries to be multivariate polynomials, and by determining not only the determinant but also the Smith normal form of these matrices. A priori t...
متن کاملSmith Normal Form of a Multivariate Matrix Associated with Partitions (preliminary version)
E. R. Berlekamp [1][2] raised a question concerning the entries of certain matrices of determinant 1. (Originally Berlekamp was interested only in the entries modulo 2.) Carlitz, Roselle, and Scoville [3] gave a combinatorial interpretation of the entries (over the integers, not just modulo 2) in terms of lattice paths. Here we will generalize the result of Carlitz, Roselle, and Scoville in two...
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 کاملThe Smith Normal Form of a Matrix Associated with Young’s Lattice
Let R be a commutative ring with 1 and M an m×m matrix over R. We say that M has a Smith normal form (SNF) over R if there exist matrices P,Q ∈ SL(m,R) (so detP = detQ = 1) such that PMQ is a diagonal matrix diag(d1, d2, . . . , dm) with di | di+1 (1 ≤ i ≤ m − 1) in R. It is wellknown that if R is an integral domain and if the SNF of M exists, then it is unique up to multiplication of each di b...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2014
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-014-0527-4