کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776947 | 1413646 | 2017 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A recursion on maximal chains in the Tamari lattices
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: A recursion on maximal chains in the Tamari lattices A recursion on maximal chains in the Tamari lattices](/preview/png/5776947.png)
چکیده انگلیسی
The Tamari lattices have been intensely studied since their introduction by Dov Tamari around 1960. However oddly enough, a formula for the number of maximal chains is still unknown. This is due largely to the fact that maximal chains in the nth Tamari lattice Tn range in length from nâ1 to n2. In this note, we treat vertices in the lattice as Young diagrams and identify maximal chains as certain tableaux. For each iâ¥â1, we define Ci(n) as the set of maximal chains in Tn of length n+i. We give a recursion for #Ci(n) and an explicit formula based on predetermined initial values. The formula is a polynomial in n of degree 3i+3. For example, the number of maximal chains of length n in Tn is #C0(n)=n3. The formula has a combinatorial interpretation in terms of a special property of maximal chains.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 340, Issue 4, April 2017, Pages 661-677
Journal: Discrete Mathematics - Volume 340, Issue 4, April 2017, Pages 661-677
نویسندگان
Luke Nelson,