Geodesic
Shifting operations and graded Betti numbers
Journal of Algebraic Combinatorics, Tome 12 (2000) no. 3, pp. 207-222.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The behaviour of graded Betti numbers under exterior and symmetric algebraic shifting is studied. It is shown that the extremal Betti numbers are stable under these operations. Moreover, the possible sequences of super extremal Betti numbers for a graded ideal with given Hilbert function are characterized. Finally it is shown that over a field of characteristic 0, the graded Betti numbers of a squarefree monomial ideal are bounded by those of the corresponding squarefree lexsegment ideal.
Keywords: algebraic shifting, shifted complexes, generic initial ideals, extremal Betti numbers 
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     author = {Aramova, Annetta and Herzog, J\"urgen and Hibi, Takayuki},
     title = {Shifting operations and graded {Betti} numbers},
     journal = {Journal of Algebraic Combinatorics},
     pages = {207--222},
     publisher = {mathdoc},
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     year = {2000},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2000__12_3_a5/}
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Aramova, Annetta; Herzog, Jürgen; Hibi, Takayuki. Shifting operations and graded Betti numbers. Journal of Algebraic Combinatorics, Tome 12 (2000) no. 3, pp. 207-222. http://geodesic.mathdoc.fr/item/JAC_2000__12_3_a5/