Nonsymmetric Operads In Combinatorics

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Nonsymmetric Operads in Combinatorics

Samuele Giraudo
Nonsymmetric Operads in Combinatorics Book PDF

Author : Samuele Giraudo
Publisher : Springer
Page : 172 pages
File Size : 55,8 Mb
Release : 2019-01-04
Category : Mathematics
ISBN : 9783030020743

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Nonsymmetric Operads in Combinatorics by Samuele Giraudo Pdf

Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form more complex ones. Coming historically from algebraic topology, operads intervene now as important objects in computer science and in combinatorics. A lot of operads involving combinatorial objects highlight some of their properties and allow to discover new ones. This book portrays the main elements of this theory under a combinatorial point of view and exposes the links it maintains with computer science and combinatorics. Examples of operads appearing in combinatorics are studied. The modern treatment of operads consisting in considering the space of formal power series associated with an operad is developed. Enrichments of nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.

Set Operads in Combinatorics and Computer Science

Miguel A. Méndez
Set Operads in Combinatorics and Computer Science Book PDF

Author : Miguel A. Méndez
Publisher : Springer
Page : 129 pages
File Size : 45,8 Mb
Release : 2015-01-08
Category : Mathematics
ISBN : 9783319117133

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Set Operads in Combinatorics and Computer Science by Miguel A. Méndez Pdf

This monograph has two main objectives. The first one is to give a self-contained exposition of the relevant facts about set operads, in the context of combinatorial species and its operations. This approach has various advantages: one of them is that the definition of combinatorial operations on species, product, sum, substitution and derivative, are simple and natural. They were designed as the set theoretical counterparts of the homonym operations on exponential generating functions, giving an immediate insight on the combinatorial meaning of them. The second objective is more ambitious. Before formulating it, authors present a brief historic account on the sources of decomposition theory. For more than forty years decompositions of discrete structures have been studied in different branches of discrete mathematics: combinatorial optimization, network and graph theory, switching design or boolean functions, simple multi-person games and clutters, etc.

New Trends In Algebras And Combinatorics - Proceedings Of The Third International Congress In Algebras And Combinatorics (Icac2017)

Shum Kar Ping,Zelmanov Efim,Kolesnikov Pavel,Wong Anita S M
New Trends In Algebras And Combinatorics Proceedings Of The Third International Congress In Algebras And Combinatorics Icac2017 Book PDF

Author : Shum Kar Ping,Zelmanov Efim,Kolesnikov Pavel,Wong Anita S M
Publisher : World Scientific
Page : 500 pages
File Size : 47,7 Mb
Release : 2020-02-18
Category : Mathematics
ISBN : 9789811215483

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New Trends In Algebras And Combinatorics - Proceedings Of The Third International Congress In Algebras And Combinatorics (Icac2017) by Shum Kar Ping,Zelmanov Efim,Kolesnikov Pavel,Wong Anita S M Pdf

This volume composed of twenty four research articles which are selected from the keynote speakers and invited lectures presented in the 3rd International Congress in Algebra and Combinatorics (ICAC2017) held on 25-28 August 2017 in Hong Kong and one additional invited article. This congress was specially dedicated to Professor Leonid Bokut on the occasion of his 80th birthday.

Combinatorics and Physics

Kurusch Ebrahimi-Fard
Combinatorics and Physics Book PDF

Author : Kurusch Ebrahimi-Fard
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 50,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853290

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Combinatorics and Physics by Kurusch Ebrahimi-Fard Pdf

This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition

Anonim
Issues in Logic Probability Combinatorics and Chaos Theory 2013 Edition Book PDF

Author : Anonim
Publisher : ScholarlyEditions
Page : 1001 pages
File Size : 41,9 Mb
Release : 2013-05-01
Category : Mathematics
ISBN : 9781490110127

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Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition by Anonim Pdf

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Algebraic Operads

Murray R. Bremner,Vladimir Dotsenko
Algebraic Operads Book PDF

Author : Murray R. Bremner,Vladimir Dotsenko
Publisher : CRC Press
Page : 382 pages
File Size : 50,5 Mb
Release : 2016-04-06
Category : Mathematics
ISBN : 9781482248579

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Algebraic Operads by Murray R. Bremner,Vladimir Dotsenko Pdf

Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Grobner bases in several contexts. The book builds up to the theory of Grobner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. The authors present a variety of topics including: non

Colored Operads

Donald Yau
Colored Operads Book PDF

Author : Donald Yau
Publisher : American Mathematical Soc.
Page : 428 pages
File Size : 55,7 Mb
Release : 2016-02-29
Category : Algebra, Homological
ISBN : 9781470427238

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Colored Operads by Donald Yau Pdf

The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. A (colored) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). Topics covered include basic graph theory, basic category theory, colored operads, and algebras over colored operads. Free colored operads are discussed in complete detail and in full generality. The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.

Algebraic Operads

Jean-Louis Loday,Bruno Vallette
Algebraic Operads Book PDF

Author : Jean-Louis Loday,Bruno Vallette
Publisher : Springer Science & Business Media
Page : 649 pages
File Size : 42,5 Mb
Release : 2012-08-08
Category : Mathematics
ISBN : 9783642303623

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Algebraic Operads by Jean-Louis Loday,Bruno Vallette Pdf

In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.

Operads in Algebra, Topology and Physics

Martin Markl,Steven Shnider,James D. Stasheff
Operads in Algebra Topology and Physics Book PDF

Author : Martin Markl,Steven Shnider,James D. Stasheff
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 44,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821843628

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Operads in Algebra, Topology and Physics by Martin Markl,Steven Shnider,James D. Stasheff Pdf

Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.

On Operads, Bimodules and Analytic Functor

Nicola Gambino,André Joyal
On Operads Bimodules and Analytic Functor Book PDF

Author : Nicola Gambino,André Joyal
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 44,6 Mb
Release : 2017-09-25
Category : Algebra, Homological
ISBN : 9781470425760

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On Operads, Bimodules and Analytic Functor by Nicola Gambino,André Joyal Pdf

The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory of operad bimodules, that has operads as -cells, operad bimodules as -cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. In order to obtain this result, the authors extend the theory of distributors and the formal theory of monads.

Simplicial Methods for Operads and Algebraic Geometry

Ieke Moerdijk,Bertrand Toën
Simplicial Methods for Operads and Algebraic Geometry Book PDF

Author : Ieke Moerdijk,Bertrand Toën
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 52,5 Mb
Release : 2010-12-01
Category : Mathematics
ISBN : 9783034800525

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Simplicial Methods for Operads and Algebraic Geometry by Ieke Moerdijk,Bertrand Toën Pdf

"This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"--Foreword

Leavitt Path Algebras and Classical K-Theory

A. A. Ambily,Roozbeh Hazrat,B. Sury
Leavitt Path Algebras and Classical K Theory Book PDF

Author : A. A. Ambily,Roozbeh Hazrat,B. Sury
Publisher : Springer Nature
Page : 340 pages
File Size : 48,7 Mb
Release : 2020-01-17
Category : Mathematics
ISBN : 9789811516115

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Leavitt Path Algebras and Classical K-Theory by A. A. Ambily,Roozbeh Hazrat,B. Sury Pdf

The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.

Operads and Universal Algebra

Chengming Bai
Operads and Universal Algebra Book PDF

Author : Chengming Bai
Publisher : World Scientific
Page : 318 pages
File Size : 47,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814365123

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Operads and Universal Algebra by Chengming Bai Pdf

The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.

Topics in Theoretical Computer Science

Mohammad Reza Mousavi,Jiří Sgall
Topics in Theoretical Computer Science Book PDF

Author : Mohammad Reza Mousavi,Jiří Sgall
Publisher : Springer
Page : 139 pages
File Size : 53,7 Mb
Release : 2017-10-12
Category : Computers
ISBN : 9783319689531

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Topics in Theoretical Computer Science by Mohammad Reza Mousavi,Jiří Sgall Pdf

This book constitutes the refereed proceedings of the Second IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science, TTCS 2017, held in Tehran, Iran, in September 2017. The 8 papers presented in this volume were carefully reviewed and selected from 20 submissions. They were organized in topical sections named: algorithms and complexity; and logic, semantics, and programming theory.

Dialgebras and Related Operads

J.-L. Loday,A. Frabetti,F. Chapoton,F. Goichot
Dialgebras and Related Operads Book PDF

Author : J.-L. Loday,A. Frabetti,F. Chapoton,F. Goichot
Publisher : Springer
Page : 140 pages
File Size : 52,7 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540453284

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Dialgebras and Related Operads by J.-L. Loday,A. Frabetti,F. Chapoton,F. Goichot Pdf

The main object of study of these four papers is the notion of associative dialgebras which are algebras equipped with two associative operations satisfying some more relations of the associative type. This notion is studied from a) the homological point of view: construction of the (co)homology theory with trivial coefficients and general coefficients, b) the operadic point of view: determination of the dual operad, that is the dendriform dialgebras which are strongly related with the planar binary trees, c) the algebraic point of view: Hopf structure and Milnor-Moore type theorem.