Some Combinatorial Identities from the Random Walk

TL;DR

This paper presents eight combinatorial identities derived from counting paths in a one-dimensional random walk, with four identities potentially being novel contributions to the field.

Contribution

The paper introduces four new combinatorial identities proven through path counting in one-dimensional random walks.

Findings

Eight identities listed and proved

Four identities are potentially new

Method based on path counting in random walks

Abstract

Eight combinatorial identities are listed and proved by counting paths in the one-dimensional random walk. Four of these identities are assumed to be new.