An Atlas of the Smaller Maps in Orientable and Nonorientable by David Jackson,Terry I. Visentin

By David Jackson,Terry I. Visentin

Maps are beguilingly easy buildings with deep and ubiquitous houses. They come up in an important manner in lots of parts of arithmetic and mathematical physics, yet require massive time and computational attempt to generate. Few accumulated drawings can be found for reference, and little has been written, in ebook shape, approximately their enumerative features.

An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces is the 1st booklet to supply whole 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 advent to maps as a combinatorial constitution. The Atlas lists the maps first via genus and variety of edges, and offers the embeddings of all graphs with at so much 5 edges in orientable surfaces, therefore offering the genus distribution for every graph. Exemplifying using the Atlas, the authors discover colossal conjectures with origins in mathematical physics and geometry: the Quadrangulation Conjecture and the b-Conjecture.

The authors' transparent, readable exposition and assessment of enumerative concept makes this assortment obtainable even to execs who're now not experts. For researchers and scholars operating with maps, the Atlas offers a prepared resource of knowledge for trying out conjectures and exploring the algorithmic and algebraic houses of maps.

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