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Symmetric Boolean functions have played an important role in many aspects of design automation for many years. This book summarizes developments and provides a collection of new tools and techniques that can be used to advance the study of Boolean functions. Moreover, Boolean functions provide the necessary framework for expressing the operation of logic gates, which are the key building units for the accomplishment of signal processing tasks in fundamental and system-oriented levels. The book concludes with a discussion on how Boolean functions can be used to ensure the minimum degree of logi

Algebra, Boolean. --- Symmetric functions. --- Functions, Symmetric --- Equations, Theory of --- Boolean algebra --- Boole's algebra --- Algebraic logic --- Set theory

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This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Symmetric functions. --- Sequences (Mathematics) --- Functions, Special. --- Combinatorial analysis. --- Combinatorics --- Special functions --- Mathematical sequences --- Numerical sequences --- Functions, Symmetric --- Mathematics. --- Sequences (Mathematics). --- Special functions. --- Combinatorics. --- Special Functions. --- Sequences, Series, Summability. --- Mathematical analysis --- Equations, Theory of --- Functions, special.

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331.5 --- Labor market --- -Labor market --- -Symmetric functions --- Functions, Symmetric --- Equations, Theory of --- Employees --- Market, Labor --- Supply and demand for labor --- Markets --- Arbeidsmarkt. Werkgelegenheid --(algemeen) --- Econometric models --- Simulation methods --- Supply and demand --- Theses --- Symmetric functions. --- Econometric models. --- Simulation methods. --- 331.5 Arbeidsmarkt. Werkgelegenheid --(algemeen) --- Symmetric functions

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Categories (Mathematics) --- Quantum groups. --- Symmetric functions. --- Finite fields (Algebra) --- Catégories (Mathématiques) --- Groupes quantiques --- Fonctions symétriques --- Corps finis --- Group theory --- Quantum groups --- Symmetric functions --- 51 <082.1> --- Functions, Symmetric --- Equations, Theory of --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Mathematical physics --- Quantum field theory --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Modules (Algebra) --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Mathematics--Series