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- W1646579992 abstract "Let M in k[x,y] be a monomial ideal M=(m_1,m_2,...,m_r), where the m_i are a minimal generating set of M. We construct an explicit free resolution of k over S=k[x,y]/M for all monomial ideals M, and provide recursive formulas for the Betti numbers. In particular, if M is any monomial ideal (excepting five degenerate cases,) the total Betti numbers beta_i^S(k) are given by beta_0^S(k)=1, beta_1^S(k)=2, and beta_i^S(k)=beta_{i-1}(k)+(r-1)beta_{i-2}^S(k), where r is the number of minimal generators of M. This specializes to the classic example S=k[x,y]/(x^2,xy), which has beta_i^S(k)=F_{i+1}, where F_{i+1} is the (i+1)st Fibonacci number. Macaulay2 code producing these resolutions is available at: this http URL" @default.
- W1646579992 created "2016-06-24" @default.
- W1646579992 creator A5086438771 @default.
- W1646579992 date "2013-08-01" @default.
- W1646579992 modified "2023-09-27" @default.
- W1646579992 title "Infinite Free Resolutions over Monomial Rings in Two Variables" @default.
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- W1646579992 hasPublicationYear "2013" @default.
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