Reverse lexicographic and lexicographic shifting
Reverse lexicographic and lexicographic shifting
复制标题
反向字典顺序和字典顺序移位
DOI：
10.1007/s10801-006-6919-3
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发表时间：
2005
影响因子：
0.8
通讯作者：
Rekha R. Thomas
中科院分区：
文献类型：
--
作者：
E. Babson;I. Novik;Rekha R. Thomas
A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, Δlex-an operation that transforms a monomial ideal of S = K[xi: i ∈ 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 ⊂ 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 $$\{ \Delta_{\rm lex}^{i} (I) \}_{i=0}^{\infty}$$} are distinct. The limit ideal $$\bar{\Delta}(I) = {\rm lim}_{i \rightarrow \infty} \Delta_{\rm lex}^{i} (I)$$ is well defined and is a USLI that depends only on a certain analog of the Hilbert function of I.
A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, Δlex—an operation that transforms a monomial ideal of S = K[xi: i ∈ 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 ⊂ 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 $$\{ \Delta_{\rm lex}^{i} (I) \}_{i=0}^{\infty}$$} are distinct. The limit ideal $$\bar{\Delta}(I) = {\rm lim}_{i \rightarrow \infty} \Delta_{\rm lex}^{i} (I)$$ is well defined and is a USLI that depends only on a certain analog of the Hilbert function of I.
DOI：
--
发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
--
作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest