Walaa Asakly

collaborators

3 papers

math.CO2025

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 $[n]$ with exactly $k$ blocks, as well as an asymp…

math.CO2025

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 $π = π_{1} π_{2} \dots π_{n}$ of length $n$ over the alphabet $[k]$ , a k-connector is defined as an o…

math.CO2019

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 $[n]$ in terms of Bell numbe…