Reverse lexicographic and lexicographic shifting

Babson, Eric; Novik, Isabella; Thomas, Rekha

Geodesic

Parcourir par

Reverse lexicographic and lexicographic shifting

Babson, Eric ; Novik, Isabella ; Thomas, Rekha

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

Résumé

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,

Δ_{l e x}

-an operation that transforms a monomial ideal of

S = K [x_{i}

: i

\in 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_

lex^i (I) }_i=0^infty are distinct. The limit ideal [ `

(D)] (I) = l i m_{i ® \?}

_{l e x}^{i} (I)

barDelta$(I) = {\rm $lim_i

\to

infty Delta_

lex^i (I) is well defined and is a USLI that depends only on a certain analog of the Hilbert function of

I

Mots-clés : keywords shifting, reverse lexicographic

@article{JAC_2006__23_2_a5,
     author = {Babson, Eric and Novik, Isabella and Thomas, Rekha},
     title = {Reverse lexicographic and lexicographic shifting},
     journal = {Journal of Algebraic Combinatorics},
     pages = {107--123},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2006},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/JAC_2006__23_2_a5/}
}

TY  - JOUR
AU  - Babson, Eric
AU  - Novik, Isabella
AU  - Thomas, Rekha
TI  - Reverse lexicographic and lexicographic shifting
JO  - Journal of Algebraic Combinatorics
PY  - 2006
SP  - 107
EP  - 123
VL  - 23
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/JAC_2006__23_2_a5/
LA  - en
ID  - JAC_2006__23_2_a5
ER  -

%0 Journal Article
%A Babson, Eric
%A Novik, Isabella
%A Thomas, Rekha
%T Reverse lexicographic and lexicographic shifting
%J Journal of Algebraic Combinatorics
%D 2006
%P 107-123
%V 23
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/JAC_2006__23_2_a5/
%G en
%F JAC_2006__23_2_a5

Babson, Eric; Novik, Isabella; Thomas, Rekha. Reverse lexicographic and lexicographic shifting. Journal of Algebraic Combinatorics, Tome 23 (2006) no. 2, pp. 107-123. https://geodesic-test.mathdoc.fr/item/JAC_2006__23_2_a5/