Primary Decomposition of Ideals Arising from Hankel Matrices
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摘要
Hankel matrices have many applications in various elds ranging from engi- neering to computer science. Their internal structure gives them many special properties. In this paper we focus on the structure of the set of polynomials generated by the minors of generalized Hankel matrices whose entries consist of indeterminates with coecients from a eld k. A generalized Hankel matrix M has in its jth codiagonal constant multiples of a single variable Xj. Consider now the ideal Ir(M) in the polynomial ring k(X1;:::;Xm+n 1) generated by all (r r)-minors of M. An important structural feature of the ideal Ir(M) is its primary decomposition into an intersection of primary ideals. This decom- position is analogous to the decomposition of a positive integer into a product of prime powers. Just like factorization of integers into primes, the primary de- composition of an ideal is very dicult to compute in general. Recent studies have described the structure of the primary decomposition of I2(M). However, the case whenr > 2 is substantially more complicated. We will present an anal- ysis of the primary decomposition of I3(M) for generalized Hankel matrices up to size 5 5.
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