Geodesic
Betti numbers of lex ideals over some Macaulay-lex rings
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 2, pp. 299-318.

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

Summary: Let $A= K[ x _{1},\cdots , x _{ n }]$ be a polynomial ring over a field $K$ and $M$ a monomial ideal of $A$. The quotient ring $R= A/ M$ is said to be Macaulay-Lex if every Hilbert function of a homogeneous ideal of $R$ is attained by a lex ideal. In this paper, we introduce some new Macaulay-Lex rings and study the Betti numbers of lex ideals of those rings. In particular, we prove a refinement of the Frankl-Füredi-Kalai Theorem which characterizes the face vectors of colored complexes. Additionally, we disprove a conjecture of Mermin and Peeva that lex-plus- $M$ ideals have maximal Betti numbers when $A/ M$ is Macaulay-Lex.
Keywords: keywords lex ideals, graded Betti numbers, Hilbert functions, colored simplicial complexes 
@article{JAC_2010__31_2_a0,
     author = {Mermin, Jeff and Murai, Satoshi},
     title = {Betti numbers of lex ideals over some {Macaulay-lex} rings},
     journal = {Journal of Algebraic Combinatorics},
     pages = {299--318},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__31_2_a0/}
}
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Mermin, Jeff; Murai, Satoshi. Betti numbers of lex ideals over some Macaulay-lex rings. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 2, pp. 299-318. http://geodesic.mathdoc.fr/item/JAC_2010__31_2_a0/