کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777567 | 1632924 | 2017 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Bell numbers, partition moves and the eigenvalues of the random-to-top shuffle in Dynkin Types A, B and D
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Bell numbers, partition moves and the eigenvalues of the random-to-top shuffle in Dynkin Types A, B and D Bell numbers, partition moves and the eigenvalues of the random-to-top shuffle in Dynkin Types A, B and D](/preview/png/5777567.png)
چکیده انگلیسی
Let Bt(n) be the number of set partitions of a set of size t into at most n parts and let Btâ²(n) be the number of set partitions of {1,â¦,t} into at most n parts such that no part contains both 1 and t or both i and i+1 for any iâ{1,â¦,tâ1}. We give two new combinatorial interpretations of the numbers Bt(n) and Btâ²(n) using sequences of random-to-top shuffles, and sequences of box moves on the Young diagrams of partitions. Using these ideas we obtain a very short proof of a generalization of a result of Phatarfod on the eigenvalues of the random-to-top shuffle. We also prove analogous results for random-to-top shuffles that may flip certain cards. The proofs use the Solomon descent algebras of Types A, B and D. We give generating functions and asymptotic results for all the combinatorial quantities studied in this paper.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 148, May 2017, Pages 116-144
Journal: Journal of Combinatorial Theory, Series A - Volume 148, May 2017, Pages 116-144
نویسندگان
John R. Britnell, Mark Wildon,