# Counting birthday collisions using partitions

## TL;DR

This paper introduces partition-based formulas to analyze the probability of s-collisions in the Birthday Problem, offering new mathematical tools for understanding birthday collision events.

## Contribution

It presents novel partition-based formulas for counting s-collisions and related events in the Birthday Problem, advancing theoretical understanding.

## Key findings

- Derived formulas for s-collision counts
- Enhanced mathematical understanding of birthday collisions
- Applicable to various forms of the Birthday Problem

## Abstract

We use partitions to provide some formulae for counting s-collisions and other events in various forms of the Birthday Problem.