Perfect snake-in-the-box codes for rank modulation
Combinatorics
2016-10-18 v3 Information Theory
Group Theory
math.IT
Abstract
For odd n, the alternating group on n elements is generated by the permutations that jump an element from any odd position to position 1. We prove Hamiltonicity of the associated directed Cayley graph for all odd n not equal to 5. (A result of Rankin implies that the graph is not Hamiltonian for n=5.) This solves a problem arising in rank modulation schemes for flash memory. Our result disproves a conjecture of Horovitz and Etzion, and proves another conjecture of Yehezkeally and Schwartz.
Cite
@article{arxiv.1602.08073,
title = {Perfect snake-in-the-box codes for rank modulation},
author = {Alexander E. Holroyd},
journal= {arXiv preprint arXiv:1602.08073},
year = {2016}
}