4 papers · 1 filter
Sum of elements preceding records in set partitions
Walaa Asakly, Noor Kezil
In this paper, we aim to derive an explicit formula for the total number of elements preceding records over all set partitions of with exactly blocks, as well as an asymp…
Enumerating k-connected blocks and gk-connected blocks in words
Walaa Asakly, Noor Kezil
We define two new statistics on words: the k-connector and the gk-connector. For a word of length over the alphabet , a k-connector is defined as an o…
Counting symmetric and non-symmetric peaks in a set partition
Walaa Asakly, Noor Kezil
The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of with exactly blocks,…
Sum of weighted records in set partitions
Walaa Asakly
The purpose of this paper is to find an explicit formula and asymptotic estimate for the total number of sum of weighted records over set partitions of in terms of Bell numbe…