Khayyam-Pascal Determinantal Arrays, Star of David Rule and Log-Concavity

TL;DR

This paper introduces a geometric approach to analyze the log-concavity of combinatorial sequences derived from Pascal's triangle, providing new insights into their structural properties.

Contribution

It presents a novel geometric method for investigating log-concavity in Pascal-related combinatorial sequences, advancing theoretical understanding.

Findings

Established log-concavity for new classes of sequences

Connected geometric properties with combinatorial log-concavity

Provided a framework for future research in combinatorial geometry

Abstract

In this paper we develop a new geometric method to answer the log-concavity questions related to a nice class of combinatorial sequences arising from the Pascal triangle.