By David Jackson,Terry I. Visentin

Maps are beguilingly uncomplicated constructions with deep and ubiquitous houses. They come up in an important approach in lots of parts of arithmetic and mathematical physics, yet require huge time and computational attempt to generate. Few accrued drawings can be found for reference, and little has been written, in booklet shape, approximately their enumerative points.

An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces is the 1st ebook to supply entire collections of maps besides their vertex and face walls, variety of rootings, and an index quantity for move referencing. It presents a proof of axiomatization and encoding, and serves as an creation to maps as a combinatorial constitution. The Atlas lists the maps first by means of genus and variety of edges, and offers the embeddings of all graphs with at so much 5 edges in orientable surfaces, hence proposing the genus distribution for every graph. Exemplifying using the Atlas, the authors discover vast conjectures with origins in mathematical physics and geometry: the Quadrangulation Conjecture and the b-Conjecture.

The authors' transparent, readable exposition and evaluate of enumerative concept makes this assortment available even to pros who're no longer experts. For researchers and scholars operating with maps, the Atlas offers a prepared resource of information for trying out conjectures and exploring the algorithmic and algebraic homes of maps.

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