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TitleCombinatorial Aspects of Total Weight Orders over Monomials of Fixed Degree
Author(s) Andrea Vietri
TypeArticle in Journal
AbstractAmong all the restrictions of weight orders to the subsets of monomials with a fixed degree, we consider those that yield a total order. Furthermore, we assume that each weight vector consists of an increasing tuple of weights. Every restriction, which is shown to be achieved by some monomial order, is interpreted as a suitable linearization of the poset arising by the intersection of all the weight orders. In the case of three variables, an enumeration is provided. For a higher number of variables, we show a necessary condition for obtaining such restrictions, using deducibility rules applied to homogeneous inequalities. The logarithmic version of this approach is deeply related to classical results of Farkas type, on systems of linear inequalities. Finally, we analyze the linearizations determined by sequences of prime numbers and provide some connections with topics in arithmetic.
Keywordsbeta-linearization, coloring, Gröbner bases, linear inequalities, logical consequence, monomial ordering, primes, weight order
Length25
ISSN0167-8094
File
URL dx.doi.org/10.1023/A:1021236722756
LanguageEnglish
JournalOrder
Volume19
Number3
Pages239-263
PublisherSpringer Science Business Media B.V.
Year2002
MonthSeptember
Translation No
Refereed No
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