کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896429 | 1630415 | 2018 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Root multiplicities for Borcherds algebras and graph coloring
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We establish a connection between root multiplicities for Borcherds-Kac-Moody algebras and graph coloring. We show that the generalized chromatic polynomial of the graph associated to a given Borcherds algebra can be used to give a closed formula for certain root multiplicities. Using this connection we give a second interpretation, namely that the root multiplicity of a given root coincides with the number of acyclic orientations with a unique sink of a certain graph (depending on the root). Finally, using the combinatorics of Lyndon words we construct a basis for the root spaces corresponding to these roots and determine the Hilbert series in the case when all simple roots are imaginary. As an application we give a Lie theoretic proof of Stanley's reciprocity theorem of chromatic polynomials.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 499, 1 April 2018, Pages 538-569
Journal: Journal of Algebra - Volume 499, 1 April 2018, Pages 538-569
نویسندگان
G. Arunkumar, Deniz Kus, R. Venkatesh,