A formula for the base size of the symmetric group in its action on subsets

TL;DR

This paper derives a formula for the minimal number of points needed to uniquely determine the symmetric group acting on k-subsets, and computes these values explicitly for small k.

Contribution

The paper provides a new explicit formula for the base size of the symmetric group acting on k-subsets, and calculates these sizes for all n and k ≤ 14.

Findings

Derived a formula for the base size of the symmetric group on k-subsets

Computed base sizes explicitly for all n and k ≤ 14

Enhanced understanding of permutation group actions

Abstract

Given two positive integers $n$ and $k$, we obtain a formula for the base size of the symmetric group of degree $n$ in its action on $k$-subsets. Then, we use this formula to compute explicitly the base size for each $n$ and for each $k\le 14$.