The Smith normal form of a matrix associated with Young’s lattice
نویسندگان
چکیده
منابع مشابه
The 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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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...
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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...
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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...
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Let JTλ be the Jacobi-Trudi matrix corresponding to the partition λ, so det JTλ is the Schur function sλ in the variables x1, x2, . . . . Set x1 = · · · = xn = 1 and all other xi = 0. Then the entries of JTλ become polynomials in n of the form ( n+j−1 j ) . We determine the Smith normal form over the ring Q[n] of this specialization of JTλ . The proof carries over to the specialization xi = q i...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/12642