کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4583806 | 1630457 | 2016 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Automata, reduced words and Garside shadows in Coxeter groups
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Automata, reduced words and Garside shadows in Coxeter groups Automata, reduced words and Garside shadows in Coxeter groups](/preview/png/4583806.png)
چکیده انگلیسی
In this article, we introduce and investigate a class of finite deterministic automata that all recognize the language of reduced words of a finitely generated Coxeter system (W,S). The definition of these automata is straightforward as it only requires the notion of weak order on (W,S) and the related notion of Garside shadows in (W,S), an analog of the notion of a Garside family. Then we discuss the relations between this class of automata and the canonical automaton built from Brink and Howlett's small roots. We end this article by providing partial positive answers to two conjectures: (1) the automata associated to the smallest Garside shadow is minimal; (2) the canonical automaton is minimal if and only if the support of all small roots is spherical, i.e., the corresponding root system is finite.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 457, 1 July 2016, Pages 431-456
Journal: Journal of Algebra - Volume 457, 1 July 2016, Pages 431-456
نویسندگان
Christophe Hohlweg, Philippe Nadeau, Nathan Williams,