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arXiv · 2007.05870

A subquadratic algorithm for the simultaneous conjugacy problem

Andrej Brodnik·Aleksander Malnič·Rok Požar
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Abstract

The $d$-Simultaneous Conjugacy problem in the symmetric group $S_n$ asks whether there exists a permutation $\tau \in S_n$ such that $b_j = \tau^{-1}a_j \tau$ holds for all $j = 1,2,\ldots, d$, where $a_1, a_2,\ldots , a_d$ and $b_1, b_2,\ldots , b_d$ are given sequences of permutations in $S_n$. The time complexity of existing algorithms for solving the problem is $O(dn^2)$. We show that for a given positive integer $d$ the $d$-Simultaneous Conjugacy problem in $S_n$ can be solved in $o(n^2)$ time.

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Andrej Brodnik, Aleksander Malnič, Rok Požar. 2020-07-11. A subquadratic algorithm for the simultaneous conjugacy problem. https://arxiv.org/abs/2007.05870

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