A New Universal Cycle for Permutations

Document Type

Article

Publication Date

11-1-2017

Abstract

We introduce a novel notation, the relaxed shorthand notation, to encode permutations. We then present a simple shift rule that exhaustively lists out each of the permutations exactly once. The shift rule induces a cyclic Gray code for permutations where successive strings differ by a rotation or a shift. By concatenating the first symbol of each string in the listing, we produce a universal cycle for permutations in relaxed shorthand notation. We also prove that the universal cycle can be constructed in O(1)-amortized time per symbol using O(n) space.

Publication Title

Graphs and Combinatorics

First Page Number

1393

Last Page Number

1399

DOI

10.1007/s00373-017-1778-3

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