Kategoria BISAC: Mathematics >> Combinatorics

This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition.
Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important...

The purpose of this undergraduate textbook is to offer all the material suitable for a beginning combinatorics course for students in STEM subjects particularly mathematics and computer science, although other subjects may benefit as well. This will be achieved through the use of plentiful (though brief) examples, and a variety of exercises and problems. In addition, we use in our examples more up-to-date ideas (such as digital music files rather than books on a shelf) and give some code to assist the student with the use of Mathematica, Maple, and other technological tools.

The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.

This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.

This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.

Topics presented include:

structure and representation theory of reductive algebraic monoids

monoid schemes and applications of monoids

monoids related to Lie theory

equivariant embeddings of algebraic groups

constructions and properties of monoids from algebraic combinatorics

endomorphism monoids induced from vector bundles

Hodge-Newton decompositions of reductive...

This monograph covers some of the most important developments in Ramsey theory from its beginnings in the early 20th century via its many breakthroughs to recent important developments in the early 21st century.

The book first presents a detailed discussion of the roots of Ramsey theory before offering a thorough discussion of the role of parameter sets. It presents several examples of structures that can be interpreted in terms of parameter sets and features the most fundamental Ramsey-type results for parameter sets: Hales-Jewett's theorem and Graham-Rothschilds Ramsey theorem as...

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the...

What is grayscale coloring? Simply put, it is an easy and amazing way to add professional shading to your coloring, without having to add the shade yourself The complex gray tones add variance and depth to your art, taking your adult coloring to the next level, resulting in pictures you'll be proud to share.

• Includes 25+ beautiful photos
• Printed on one side only
• Full size (8.5"x 11"), pure white 60lb. paper

What is grayscale coloring? Simply put, it is an easy and amazing way to add professional shading to your coloring, without having to add the shade yourself The complex gray tones add variance and depth to your art, taking your adult coloring to the next level, resulting in pictures you'll be proud to share.

• Includes 25+ beautiful photos
• Printed on one side only
• Full size (8.5"x 11"), pure white 60lb. paper