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Combinatorial Identity



Polynomial Identities and Combinatorial Methods

Polynomial Identities and Combinatorial Methods
Polynomial Identities and Combinatorial Methods
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Two-Dimensional Homotopy and Combinatorial Group Theory by Cynthia Hog-Angeloni,
Two-Dimensional Homotopy and Combinatorial Group Theory by Cynthia Hog-Angeloni,
The geometric and algebraic aspects of two-dimensional homotopy theory are both important areas of current research. Basic work on two-dimensional homotopy theory dates back to Reidemeister and Whitehead. The contributors to this book consider the current state of research beginning with introductory chapters on low-dimensional topology and covering crossmodules, Peiffer-Reid identities, and concretely discussing P2 theory. The chapters have been skillfully woven together to form a coherent picture, and the geometric nature of the subject is illustrated by over 100 diagrams. The final chapters round off neatly with a look at the present status of the conjectures of Zeeman, Whitehead and Andrews-Curtis.
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Combinatorial proof - A combinatorial proof is a method of proving a statement, usually a combinatorics identity, by counting some carefully chosen object in different ways to obtain different expressions in the statement (see also double counting). Since those expressions count the same object, they must be equal to each other and thus the statement is established.

Vandermonde's identity - In combinatorial mathematics, Vandermonde's identity, named after Alexandre-Théophile Vandermonde, states that

Robinson-Schensted algorithm - In mathematics, the Robinson–Schensted algorithm is a combinatorial algorithm, first discovered by Robinson in 1938, which establishes a bijective correspondence between elements of the symmetric group S_n and pairs of standard Young tableaux of the same shape. It can be viewed as a simple, constructive proof of the combinatorial identity:

Pascal's rule - In mathematics, Pascal's rule is a combinatorial identity about binomial coefficients. It states that for any natural number n we have



combinatorialidentity

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