Sum of weighted records in set partitions
نویسندگان
چکیده
The purpose of this paper is to find an explicit formula and asymptotic estimate for the total number sum weighted records over set partitions [ n ] in terms Bell numbers. For that we study generating function according statistic records.
منابع مشابه
Records in Set Partitions
A partition of [n] = {1, 2, . . . , n} is a decomposition of [n] into nonempty subsets called blocks. We will make use of the canonical representation of a partition as a word over a finite alphabet, known as a restricted growth function. An element ai in such a word π is a strong (weak) record if ai > aj (ai > aj) for all j = 1, 2, . . . , i−1. Furthermore, the position of this record is i. We...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2021
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2020.112202