کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6424485 1343395 2012 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Proofs of two conjectures of Kenyon and Wilson on Dyck tilings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Proofs of two conjectures of Kenyon and Wilson on Dyck tilings
چکیده انگلیسی

Recently, Kenyon and Wilson introduced a certain matrix M in order to compute pairing probabilities of what they call the double-dimer model. They showed that the absolute value of each entry of the inverse matrix M−1 is equal to the number of certain Dyck tilings of a skew shape. They conjectured two formulas on the sum of the absolute values of the entries in a row or a column of M−1. In this paper we prove the two conjectures. As a consequence we obtain that the sum of the absolute values of all entries of M−1 is equal to the number of complete matchings. We also find a bijection between Dyck tilings and complete matchings.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 119, Issue 8, November 2012, Pages 1692-1710
نویسندگان
,