Jassologie : Une vision originale sur les cartes orientables

TL;DR

Jassology introduces a novel theoretical framework linking Jassologic Words to planar trivalent rooted maps, providing a bijection that enables map reconstruction solely through word-based algorithms without image processing.

Contribution

The paper presents the first formalization of Jassology, establishing a bijection between Jassologic Words and planar trivalent rooted maps, and details an algorithmic process for their conversion.

Findings

Established a bijection between Jassologic Words and maps

Developed an algorithm for map reconstruction from words

Defined a unique set of 16 characters for the process

Abstract

Jassology is a global theory on orientable maps which results from artistic experiments. The objective of this article is to define and describe the essential tools of Jassologic process, wich consists in associating a word, called Jassologic Word, to a planar trivalent rooted map. The original method is based on breaking down a map into layers of cells called "Jasses", which means "layers" in Provence. We also describe in details the set of Jassologic Words, whose alphabet is composed of 16 specified caracters (Catherine Mouet's caracters). And we explain how to construct a planar trivalent rooted map from any Jassologic Word. We obtain a bijection between Jassologic Words and the equivalence classes of planar trivalent rooted maps. In particular, two planar trivalent rooted maps are equivalent if and only if their correspondant Jassologic Words are the same. From a computer science point of view, Jassologic process is an algorithm which doesn't use any handling of images.