کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4651013 1342516 2006 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homothetic interval orders
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Homothetic interval orders
چکیده انگلیسی
We give a characterization of the non-empty binary relations ≻ on a N*-set A such that there exist two morphisms of N*-sets u1,u2:A→R+ verifying u1⩽u2 and x≻y⇔u1(x)>u2(y). They are called homothetic interval orders. If ≻ is a homothetic interval order, we also give a representation of ≻ in terms of one morphism of N*-sets u:A→R+ and a map σ:u-1(R+*)×A→R+* such that x≻y⇔σ(x,y)u(x)>u(y). The pairs (u1,u2) and (u,σ) are “uniquely” determined by ≻, which allows us to recover one from each other. We prove that ≻ is a semiorder (resp. a weak order) if and only if σ is a constant map (resp. σ=1). If moreover A is endowed with a structure of commutative semigroup, we give a characterization of the homothetic interval orders ≻ represented by a pair (u,σ) so that u is a morphism of semigroups.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 306, Issue 15, 6 August 2006, Pages 1669-1683
نویسندگان
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