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
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We give a characterization of the non-empty binary relations â» on a N*-set A such that there exist two morphisms of N*-sets u1,u2:AâR+ verifying u1⩽u2 and xâ»yâu1(x)>u2(y). They are called homothetic interval orders. If â» is a homothetic interval order, we also give a representation of â» in terms of one morphism of N*-sets u:AâR+ and a map Ï:u-1(R+*)ÃAâR+* such that xâ»yâÏ(x,y)u(x)>u(y). The pairs (u1,u2) and (u,Ï) are “uniquely” determined by â», which allows us to recover one from each other. We prove that â» is a semiorder (resp. a weak order) if and only if Ï is a constant map (resp. Ï=1). If moreover A is endowed with a structure of commutative semigroup, we give a characterization of the homothetic interval orders â» represented by a pair (u,Ï) 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
Journal: Discrete Mathematics - Volume 306, Issue 15, 6 August 2006, Pages 1669-1683
نویسندگان
Bertrand Lemaire, Marc Le Menestrel,