Boolean Representations Of Simplicial Complexes And Matroids

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Boolean Representations Of Simplicial Complexes And Matroids

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Author : John Rhodes
language : en
Publisher: Springer
Release Date : 2015-02-26

Boolean Representations Of Simplicial Complexes And Matroids written by John Rhodes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-26 with Mathematics categories.

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.

Boolean Representations Of Simplicial Complexes And Matroids

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Author : John Rhodes
language : en
Publisher:
Release Date : 2015

Boolean Representations Of Simplicial Complexes And Matroids written by John Rhodes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.

Pattern Recognition On Oriented Matroids

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Author : Andrey O. Matveev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11

Pattern Recognition On Oriented Matroids written by Andrey O. Matveev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.

Pattern Recognition on Oriented Matroids covers a range of innovative problems in combinatorics, poset and graph theories, optimization, and number theory that constitute a far-reaching extension of the arsenal of committee methods in pattern recognition. The groundwork for the modern committee theory was laid in the mid-1960s, when it was shown that the familiar notion of solution to a feasible system of linear inequalities has ingenious analogues which can serve as collective solutions to infeasible systems. A hierarchy of dialects in the language of mathematics, for instance, open cones in the context of linear inequality systems, regions of hyperplane arrangements, and maximal covectors (or topes) of oriented matroids, provides an excellent opportunity to take a fresh look at the infeasible system of homogeneous strict linear inequalities – the standard working model for the contradictory two-class pattern recognition problem in its geometric setting. The universal language of oriented matroid theory considerably simplifies a structural and enumerative analysis of applied aspects of the infeasibility phenomenon. The present book is devoted to several selected topics in the emerging theory of pattern recognition on oriented matroids: the questions of existence and applicability of matroidal generalizations of committee decision rules and related graph-theoretic constructions to oriented matroids with very weak restrictions on their structural properties; a study (in which, in particular, interesting subsequences of the Farey sequence appear naturally) of the hierarchy of the corresponding tope committees; a description of the three-tope committees that are the most attractive approximation to the notion of solution to an infeasible system of linear constraints; an application of convexity in oriented matroids as well as blocker constructions in combinatorial optimization and in poset theory to enumerative problems on tope committees; an attempt to clarify how elementary changes (one-element reorientations) in an oriented matroid affect the family of its tope committees; a discrete Fourier analysis of the important family of critical tope committees through rank and distance relations in the tope poset and the tope graph; the characterization of a key combinatorial role played by the symmetric cycles in hypercube graphs. Contents Oriented Matroids, the Pattern Recognition Problem, and Tope Committees Boolean Intervals Dehn–Sommerville Type Relations Farey Subsequences Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets Committees of Set Families, and Relative Blocking Constructions in Posets Layers of Tope Committees Three-Tope Committees Halfspaces, Convex Sets, and Tope Committees Tope Committees and Reorientations of Oriented Matroids Topes and Critical Committees Critical Committees and Distance Signals Symmetric Cycles in the Hypercube Graphs

Mathematics And Philosophy 2

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Author : Daniel Parrochia
language : en
Publisher: John Wiley & Sons
Release Date : 2023-05-09

Mathematics And Philosophy 2 written by Daniel Parrochia and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Mathematics categories.

From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use various mathematical notions of order. Throughout the book, philosophical operations and concepts are defined through examining questions relating the two kinds of known infinities – discrete and continuous – and how Woodin's approach can influence elements of philosophy. We also examine how mathematics can help a philosopher to discover the elements of stability which will help to build an image of the world, even if various approaches (for example, negative theology) generally cannot be valid. Finally, we briefly consider the possibilities of weakening formal thought represented by fuzziness and neutrosophic graphs. In a nutshell, this book expresses the importance of graphs when representing ideas and communicating them clearly with others.

Graphes Ordres Infinis Et Philosophie

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Author : Daniel Parrochia
language : fr
Publisher: ISTE Group
Release Date : 2024-01-19

Graphes Ordres Infinis Et Philosophie written by Daniel Parrochia and has been published by ISTE Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-19 with Mathematics categories.

La théorie des graphes et celle des ordres peuvent aider à décrire l’architecture des systèmes philosophiques. Après un rappel des principaux concepts en jeu, Graphes, ordres, infinis et philosophie présente quelques éléments d’histoire des graphes, allant des premières représentations aux plus contemporaines, en leur associant notamment des exemples de graphes philosophiques particuliers. Puis, la considération des ordres (partiels, totaux, arborescents) permet de tester certaines affirmations philosophiques dans le domaine existentiel (passions, désordres) ou moral (dilemmes). Via l’algèbre, la topologie, l’infini dont Spinoza ou Hegel ont fait usage, mais que les travaux de Woodin ont récemment repensés, certains concepts et systèmes philosophiques sont formellement réinterprétés. Enfin, à travers les questions de stabilité, de comparabilité et de complémentarité graphiques qui permettent d’évaluer certaines théories (par exemple la théologie négative), toute une panoplie de structures, de concepts et d’outils d’analyse est mise en place pouvant servir au philosophe ainsi qu’au mathématicien.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2006

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Boolean Algebra

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Author : R. L. Goodstein
language : en
Publisher: Courier Corporation
Release Date : 2012-08-15

Boolean Algebra written by R. L. Goodstein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-15 with Mathematics categories.

This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.

Combinatorial Algebraic Topology

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Author : Dimitry Kozlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-24

Combinatorial Algebraic Topology written by Dimitry Kozlov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-24 with Mathematics categories.

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

A Journey Through Discrete Mathematics

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Author : Martin Loebl
language : en
Publisher: Springer
Release Date : 2017-10-11

A Journey Through Discrete Mathematics written by Martin Loebl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-11 with Computers categories.

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

The Algebraic Theory Of Semigroups Volume Ii

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Author : Alfred Hoblitzelle Clifford
language : en
Publisher: American Mathematical Soc.
Release Date : 1961

The Algebraic Theory Of Semigroups Volume Ii written by Alfred Hoblitzelle Clifford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Group theory categories.