کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
12235857 | 685009 | 2018 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Representation of lattices via set-colored posets
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
This paper proposes a representation theory for any finite lattice via set-colored posets, in the spirit of Birkhoff for distributive lattices. The notion of colored posets was introduced in Nourine (2000) [34] and the generalization to set-colored posets was given in Nourine (2000) [35]. In this paper, we give a characterization of set-colored posets for general lattices, and show that set-colored posets capture the order induced by join-irreducible elements of a lattice as Birkhoff's representation does for distributive lattices. We also give a classification for some lattices according to the coloring property of their set-colored representation including upper locally distributive, upper locally distributive, meet-extremal and semidistributive lattices.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 249, 20 November 2018, Pages 64-73
Journal: Discrete Applied Mathematics - Volume 249, 20 November 2018, Pages 64-73
نویسندگان
Michel Habib, Lhouari Nourine,