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Advances in Combinatorial Mathematics : Proceedings of the Waterloo Workshop in Computer Algebra 2008 / edited by Ilias S. Kotsireas, Eugene V. Zima
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2009Description: Online-Ressource (XII, 174p, digital)ISBN:- 9783642035623
- 1282459708
- 9783642035616
- 9781282459700
- 511.1 23
- 511.6
- QA155.7.E4
Contents:
Summary: Method of Coefficients: an algebraic characterization and recent applications -- Partitions With Distinct Evens -- A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings -- On multivariate Newton-like inequalities -- Niceness theorems -- Method of Generating Differentials -- Henrici’s Friendly Monster Identity Revisited -- The Automatic Central Limit Theorems Generator (and Much More!).Summary: The Second Waterloo Workshop on Computer Algebra (WWCA 2008) was held May 5-7, 2008 at Wilfrid Laurier University, Waterloo, Canada. This conference was dedicated to the 70th birthday of Georgy Egorychev (Krasnoyarsk, Russia), who is well known and highly regarded as the author of the influential, milestone book "Integral Representation and the Computation of Combinatorial Sums," which described a regular approach to combinatorial summation, today also known as the method of coefficients. Another great success of this Russian mathematician came in 1980, when he solved the van der Waerden conjecture on the determination of the minimum of the permanent of a doubly stochastic matrix and was awarded the D. R. Fulkerson Prize. This book presents a collection of selected formally refereed papers submitted after the workshop. The topics discussed in this book are closely related to Georgy Egorychev’s influential works.PPN: PPN: 1648675263Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Foreword; Preface; Contents; Method of Coefficients: an algebraic characterization and recent applications; Introduction; The method of generating functions as a method of summation (the method of coefficients); Computational scheme; Operations with formal power series and the inference rules; The problem of completeness; Connection with the theory of analytic functions; Several recent applications; The characteristic function of the stopping height for the Collatz conjecture; Computation of combinatorial sums in the theory of integral representations in Cn
Combinatorial computations related to the inversion of a system of two power series in CnAlgebraic characterization of the method of coefficients as a method of summation; References; Partitions With Distinct Evens; Introduction; Proof of Theorem 2.2; Proof of Theorem 2.3; Proof of Theorem 2.6; Conclusion; References; A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings; Introduction; Classical group characters; Auxiliary identities; Proofs of theorems; Combinatorial interpretations; More factorization theorems; References
On multivariate Newton-like inequalitiesIntroduction; Univariate Newton-like Inequalities; Propagatable sequences (weights); Multivariate Case; Generalized van der Waerden-Egorychev-Falikman lower bounds; General monomials; A lower bound on the inner products of H-Stable polynomials; Multivariate Newton Inequalities; Comments and open problems; References; Niceness theorems; Introduction and statement of the problems; Examples; Lots of compatible structure examples; Universal object examples; Niceness theorems for Hopf algebras; Large vs nice; Extremal objects and niceness
Uniqueness and rigidity and nicenessCounterexamples and paradoxical objects; An excursion into formal group theory; The amazing Witt vectors and their gracious applications; The star example: Symm; Product formulas; Some first results and theorems; Freeness theorems; On the Lazard universal formal group theorem; Objects and isomorphisms in connection with Symm; References; Method of Generating Differentials; Introduction; Variables; Free Abelian Groups; Polynomial Rings; Power Series Rings; Fields of Generalized Power Series; Differentials; Kähler Differentials; Finite Differentials
Differentials for Generalized Power SeriesResidues; Local Cohomology Residues; Logarithmic Residues; Implementations; Inverting Combinatorial Sums; Compositional Inverses and Lagrange Inversions; MacMahon's Master Theorem; Dyson's conjecture; Constraints of Analytic Functions; References; Henrici's Friendly Monster Identity Revisited; Introduction; Egorychev's Method in Action; Reduction to a single sum; Simplifying the single sum; MultiSum in Action; GeneratingFunctions in Action; Conclusion; References; The Automatic Central Limit Theorems Generator (and Much More!); References;
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