Hilbert functions and Betti numbers of reverse lexicographic ideals in the exterior algebra
Let K be a field, V a K-vector space with basis e1,...,en and let E be the exterior algebra of V. We study the class of reverse lexicographic ideals in E. We analyze the behaviour of their Hilbert functions and Betti numbers.
Anahtar Kelimeler:
Graded ring, exterior algebra, monomial ideal, minimal resolution
Hilbert functions and Betti numbers of reverse lexicographic ideals in the exterior algebra
Let K be a field, V a K-vector space with basis e1,...,en and let E be the exterior algebra of V. We study the class of reverse lexicographic ideals in E. We analyze the behaviour of their Hilbert functions and Betti numbers.
Keywords:
Graded ring, exterior algebra, monomial ideal, minimal resolution,
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- βi,j+i(E/I) = m≤n(I j+1 ) n + i− 2 n− 1 t=1 t + − t=2 ≥ m≤n(J n + i− 2 n− 1 t=1 + t − t=2 t− 1 = βi,j+i(E/J ). The required inequality follows.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
Sayıdaki Diğer Makaleler
Hilbert functions and Betti numbers of reverse lexicographic ideals in the exterior algebra
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