Geodesic
Reverse lexicographic and lexicographic shifting
Journal of Algebraic Combinatorics, Tome 23 (2006) no. 2, pp. 107-123.

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

Summary: A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, $\Delta _{lex}$-an operation that transforms a monomial ideal of $S = K[ x _{i}$: i $\in \Bbb N]$ that is finitely generated in each degree into a squarefree strongly stable ideal-is defined and studied. It is proved that (in contrast to the reverse lexicographic case) a squarefree strongly stable ideal $I \subset S$ is fixed by lexicographic shifting if and only if $I$ is a universal squarefree lexsegment ideal (abbreviated USLI) of $S$. Moreover, in the case when $I$ is finitely generated and is not a USLI, it is verified that all the ideals in the sequence D $_{ lex} ^{ i} ( I) } _{ i=0} ^{ \?}$ { Delta_$\rm $lex^i (I) }_i=0^infty are distinct. The limit ideal [ `$( D)]( I) = lim _{ i \textregistered \?}$ D $_{ lex} ^{ i} ( I)$ barDelta$(I) = {\rm $lim_i $\rightarrow $infty Delta_$\rm $lex^i (I) is well defined and is a USLI that depends only on a certain analog of the Hilbert function of $I$.
Keywords: keywords shifting, reverse lexicographic 
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     title = {Reverse lexicographic and lexicographic shifting},
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Babson, Eric; Novik, Isabella; Thomas, Rekha. Reverse lexicographic and lexicographic shifting. Journal of Algebraic Combinatorics, Tome 23 (2006) no. 2, pp. 107-123. http://geodesic.mathdoc.fr/item/JAC_2006__23_2_a5/