Convex polytopes all of whose reverse lexicographic initial ideals are squarefree
نویسندگان
چکیده
منابع مشابه
Convex Polytopes All of Whose Reverse Lexicographic Initial Ideals Are Squarefree
A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a (0, 1)-polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed (0, 1)-polytopes includes (i) hypersimplices, (ii) order polytopes of finite partially ordered sets, and (iii) stable polytopes of p...
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This article generalizes the well-known notion of generic forms to the algebra R 0 , introduced in 27]. For the total degree, then reverse lexicographic order, we prove that the initial ideal of an ideal generated by nitely many generic forms (in countably innnitely many variables) is nitely generated. This contrasts to the lexicographic order, for which initial ideals of generic ideals in gene...
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Let I be a homogeneous Artinian ideal in a polynomial ring R = k[x1, . . . , xn] over a field k of characteristic 0. We study an equivalent condition for the generic initial ideal gin(I) with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that Moreno-Socias conjecture implies Fröberg conjecture. And for the case codimI ≤ 3, we show that R/I has t...
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A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, ∆lex — 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 ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2001
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-01-05853-1