# Superpermutation matrices.

@article{Dumas2019SuperpermutationM, title={Superpermutation matrices.}, author={Guillaume Dumas}, journal={arXiv: Combinatorics}, year={2019} }

Superpermutations are words over a finite alphabet containing every permutation as a factor. Finding the minimal length of a superpermutation is still an open problem. In this article, we introduce superpermutations matrices. We establish a link between the minimal size of such a matrix and the minimal length of a universal word for the quotient of the symmetric group $S_n$ by an equivalence relation. We will then give non-trivial bounds on the minimal length of such a word and prove that the… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-9 OF 9 REFERENCES

## Tackling the Minimal Superpermutation Problem

VIEW 1 EXCERPT

## Universal cycles for permutations

VIEW 1 EXCERPT

## Containing all permutations

VIEW 2 EXCERPTS

## A LOWER BOUND ON THE LENGTH

VIEW 1 EXCERPT

## Construction of small superpermutations and minimal injective superstrings

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## A combinatorial problem

VIEW 1 EXCERPT

## Superpermutations. http://www.gregegan.net/SCIENCE/ Superpermutations/Superpermutations.html, 2018

VIEW 2 EXCERPTS

## Universal cycles for combinatorial problems

VIEW 2 EXCERPTS