Horizontal visibility graph of a random restricted growth sequence

Toufik Mansour; Reza Rastegar; Alexander Roitershtein

doi:10.1016/j.aam.2020.102145

Horizontal visibility graph of a random restricted growth sequence

Adv Appl Math. 2021 Mar:124:102145. doi: 10.1016/j.aam.2020.102145. Epub 2020 Dec 9.

Authors

Toufik Mansour¹, Reza Rastegar², Alexander Roitershtein³

Affiliations

¹ Department of Mathematics, University of Haifa, 199 Abba Khoushy Ave, 3498838 Haifa, Israel.
² Occidental Petroleum Corporation, Houston, TX 77046 and Departments of Mathematics and Engineering, University of Tulsa, OK 74104, USA.
³ Department of Statistics, Texas A&M University, College Station, TX 77843, USA.

Abstract

We study the distributional properties of horizontal visibility graphs associated with random restrictive growth sequences and random set partitions of size n. Our main results are formulas expressing the expected degree of graph nodes in terms of simple explicit functions of a finite collection of Stirling and Bernoulli numbers.

Keywords: horizontal visibility graph; partitions of a set; restricted growth function.

Grants and funding

T32 CA090301/CA/NCI NIH HHS/United States