This 1978 book gives an account of the theory of permanents, their history and applications. The volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt.

No detailed description available for "Random Permanents".

This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

This popular volume on the culture of hair through human history and around the globe has been updated and revised to include even more entries and current information. How we style our hair has the ability to shape the way others perceive us. For example, in 2017, the singer Macklemore denounced his hipster undercut hairstyle, a style that is associated with Hitler Youth and alt-right men, and in 2015, actress Rose McGowan shaved her head in order to take a stance against the traditional Hollywood sex symbol stereotype. This volume examines how hair-or lack thereof-can be an important symbol of gender, class, and culture around the world and through history. Hairstyles have come to represent cultural heritage and memory, and even political leanings, social beliefs, and identity. This second edition builds upon the original volume, updating all entries that have evolved over the last decade, such as by discussing hipster culture in the entries on beards and mustaches and recent medical breakthroughs in hair loss. New entries have been added that look at specific world regions, hair coverings, political symbolism behind certain styles, and other topics.

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

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