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The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics. The aim in this introductory textbook is to provide an accessible and wide ranging introduction to partitions, without requiring anything more of the reader than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints. The book has a short introduction followed by an initial chapter introducing Euler's famous theorem on partitions with odd parts and partitions with distinct parts. This is followed by chapters titled: Ferrers Graphs, The Rogers-Ramanujan Identities, Generating Functions, Formulas for Partition Functions, Gaussian Polynomials, Durfee Squares, Euler Refined, Plane Partitions, Growing Ferrers Boards, and Musings.

Partitions (Mathematics)

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A Diateichisma is part of a city´s fortification system. Unlike a city wall it was built within the urban area dividing a city in two parts. This study focuses on two aspects. On the one hand, the phenomenon of diateichismata is considered as part of fortification architecture, on the other hand the influence of diateichism on the organisation of the urban space is pointed out. Furthermore, the reasons, why diateichismata were build are considered as a focal point of the study. The settlement are displayed in a catalogue, technical data is in charts. Written sources mentioning diatechisma are put together including relevant passages of the text. In scientific research diateichismata have been regarded as mere functional buildings, however, they have been studied systematically.

Partitions (Mathematics)

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Modular functions. --- Partitions (Mathematics).

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Partitions (Mathematics) --- q-series

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Mathematics --- Mathematics --- Mathematics. --- Mathématiques --- Partitions (Mathematics). --- Partitions (Mathematics). --- Partitions (Mathématiques).