These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.

This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.

This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.

This modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable way with full proofs provided throughout. Step by step, the reader is guided through the intricate geometry and topology of spaces with indefinite inner product, before progressing to a presentation of the geometry and spectral theory on these spaces. The author carefully highlights where difficulties arise and what tools are available to overcome them. With generous background material included in the appendices, this text is an excellent resource for researchers in operator theory, functional analysis, and related areas as well as for graduate students.

Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.

This book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023. The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.

This book proposes a comprehensive overview of the state-of-the-art research work on multimedia analysis in IoT applications. This is a third volume by editors which provides theoretical and practical approach in the area of multimedia and IOT applications and performance analysis. Further, multimedia communication, deep learning models to multimedia data, and the new (IOT) approaches are also covered. It addresses the complete functional framework in the area of multimedia data, IoT, and smart computing techniques. It bridges the gap between multimedia concepts and solutions by providing the current IOT frameworks, their applications in multimedia analysis, the strengths and limitations of the existing methods, and the future directions in multimedia IOT analytics.

This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

Learn how to automatically prove mathematical statements in combinatorics, sequences, and number theory.