“Macaulay representation of an integer”的意思、由来-开放百科全书

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Macaulay representation of an integer

释义

References

Given positive integers and , the -th Macaulay representation of is an expression for as a sum of binomial coefficients:

Here, is a uniquely determined, strictly increasing sequence of nonnegative integers known as the Macaulay coefficients. For any two positive integers and , if and only if the sequence of Macaulay coefficients for comes before the sequence of Macaulay coefficients for in lexicographic order.

References

{{Citation | ref=Reference-idHS2006 | last=Huneke | first=Craig | last2=Swanson | first2=Irena |author2-link= Irena Swanson | title=Integral closure of ideals, rings, and modules | url=http://people.reed.edu/~iswanson/book/index.html | publisher=Cambridge University Press | location=Cambridge, UK | series=London Mathematical Society Lecture Note Series | isbn=978-0-521-68860-4 | mr=2266432 | year=2006 | volume=336 | chapter=Appendix 5 }}
{{Citation | last=Caviglia | first=Giulio | title=Commutative Algebra: Geometric, Homological, Combinatorial and Computational Aspects | url=https://books.google.com/books?id=Z0RfAU2Vw6YC&pg=PA2 | publisher=CRC Press | isbn=978-1-420-02832-4 | year=2005 | chapter=A theorem of Eakin and Sathaye and Green's hyperplane restriction theorem}}
{{Citation | last=Green | first=Mark | title=Algebraic Curves and Projective Geometry | series=Lecture Notes in Mathematics | publisher=Springer | chapter=Restrictions of linear series to hyperplanes, and some results of Macaulay and Gotzmann | doi=10.1007/BFb0085925 | isbn=978-3-540-48188-1 | year=1989}}

1 : Factorial and binomial topics

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