On the Equivalence of Three Complete Cyclic Systems of Integers

TL;DR

This paper proves the equivalence of three different complete cyclic systems of integers related to regular polygons and modular sequences, introducing a new modified modular doubling sequence and connecting it with Euler tours.

Contribution

It establishes the equivalence among three known cyclic systems and introduces a new modified modular doubling sequence with applications to Euler tours.

Findings

Proved the equivalence of three cyclic systems of integers.

Introduced a new modified modular doubling sequence.

Presented a sequence of Euler tours related to Schick's cycles.

Abstract

The system of coaches by Hilton and Pedersen, the system of cyclic sequences of Schick, and Braendli-Bayne, related to diagonals in regular (2 n)-gons, and the system of modified modular doubling sequences elaborated in this paper are proved to be equivalent. The latter system employs the modified modular equivalence used by Braendli-Bayne. A sequence of Euler tours related on Schick's cycles of diagonals is also presented.