This book contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the 3rd International Colloquium on Mathematics and Computer Science that will be held in Vienna in September 2004. It addresses a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. They will find here current questions in Computer Science and the related modern and powerful mathematical methods. The range of applications…mehr
This book contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the 3rd International Colloquium on Mathematics and Computer Science that will be held in Vienna in September 2004. It addresses a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. They will find here current questions in Computer Science and the related modern and powerful mathematical methods. The range of applications is very wide and goes beyond Computer Science.Mathematics and Computer Science III contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the Third International Colloquium on Mathematics and Computer Science, held in Vienna in September 2004. It addresses a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers.
Michael Drmota, Technische Universität Wien, Austria / Philippe Flajolet, Unité de recherche INRIA Rocquencourt, Le Chesnay Cedex, France / Danièle Gardy, Université de Versailles Saint-Quentin, Versailles, France / Bernhard Gittenberger, TU Wien, Austria
Inhaltsangabe
I. Combinatorics and Random Structures.- Common Intervals of Permutations.- Overpartitions and Generating Functions for Generalized Frobenius Partitions.- Enumerative Results on Integer Partitions Using the ECO Method.- 321-Avoiding Permutations and Chebyshev Polynomials.- Iterated Logarithm Laws and the Cycle Lengths of a Random Permutation.- Transcendence of Generating Functions of Walks on the Slit Plane.- Some Curious Extensions of the Classical Beta Integral Evaluation.- Divisor Functions and Pentagonal Numbers.- II. Graph Theory.- On Combinatorial Hoeffding Decomposition and Asymptotic Normality of Subgraph Count Statistics.- Avalanche Polynomials of Some Families of Graphs.- Perfect Matchings in Random Graphs with Prescribed Minimal Degree.- Estimating the Growth Constant of Labelled Planar Graphs.- The Number of Spanning Trees in P4-Reducible Graphs.- III. Analysis of Algorithms.- On the Stationary Search Cost for the Move-to-Root Rule with Random Weights.- Average-Case Analysis for the Probabilistic Bin Packing Problem.- Distribution of Wht Recurrences.- Probabilistic Analysis for Randomized Game Tree Evaluation.- Polynomial Time Perfect Sampling Algorithm for Two-Rowed Contingency Tables.- An Efficient Generic Algorithm for the Generation of Unlabelled Cycles.- Using Tries for Universal Data Compression.- IV. Trees.- New Strahler Numbers for Rooted Plane Trees.- An Average-Case Analysis of Basic Parameters of the Suffix Tree.- Arms and Feet Nodes Level Polynomial in Binary Search Trees.- Random Records and Cuttings in Complete Binary Trees.- Multidimensional Interval Trees.- Edit Distance between Unlabelled Ordered Trees.- Number of Vertices of a Given Outdegree in a Galton-Watson Forest.- Destruction of Recursive Trees.- V. Probability.- Restrictions on thePosition of the Maximum/Minimum in a Geometrically Distributed Sample.- Dual Random Fragmentation and Coagulation and an Application to the Genealogy of Yule Processes.- Semi-Markov Walks in Queueing and Risk Theory.- Representation of Fixed Points of a Smoothing Transformation.- Stochastic Fixed Points for the Maximum.- The Number of Descents in Samples of Geometric Random Variables.- Large Deviations for Cascades and Cascades of Large Deviations.- Partitioning with Piecewise Constant Eigenvectors.- Yaglom Type Limit Theorem for Branching Processes in Random Environment.- Two-Dimensional Limit Theorem for a Critical Catalytic Branching Random Walk.- VI. Combinatorial Stochastic Processes.- A Combinatorial Approach to Jumping Particles II: General Boundary Conditions.- Stochastic Deformations of Sample Paths of Random Walks and Exclusion Models.- A Markov Chain Algorithm for Eulerian Orientations of Planar Triangular Graphs.- Regenerative Composition Structures: Characterisation and Asymptotics of Block Counts.- Random Walks on Groups With a Tree-Like Cayley Graph.- Nested Regenerative Sets and Their Associated Fragmentation Process.- VII. Applications.- Real Numbers with Bounded Digit Averages.- Large Deviation Analysis of Space-Time Trellis Codes.- A Zero-One Law for First-Order Logic on Random Images.- Coarse and Sharp Transitions for Random Generalized Satisfyability Problems.- Stochastic Chemical Kinetics with Energy Parameters.- Large Deviations of Bellinger Distance on Partitions.- Estimation of the Offspring Mean for a General Class of Size-Dependent Branching Processes. Application to Quantitative Polymerase Chain Reaction.- A Constrained Version of Sauer's Lemma.- Author Index.
I. Combinatorics and Random Structures.- Common Intervals of Permutations.- Overpartitions and Generating Functions for Generalized Frobenius Partitions.- Enumerative Results on Integer Partitions Using the ECO Method.- 321-Avoiding Permutations and Chebyshev Polynomials.- Iterated Logarithm Laws and the Cycle Lengths of a Random Permutation.- Transcendence of Generating Functions of Walks on the Slit Plane.- Some Curious Extensions of the Classical Beta Integral Evaluation.- Divisor Functions and Pentagonal Numbers.- II. Graph Theory.- On Combinatorial Hoeffding Decomposition and Asymptotic Normality of Subgraph Count Statistics.- Avalanche Polynomials of Some Families of Graphs.- Perfect Matchings in Random Graphs with Prescribed Minimal Degree.- Estimating the Growth Constant of Labelled Planar Graphs.- The Number of Spanning Trees in P4-Reducible Graphs.- III. Analysis of Algorithms.- On the Stationary Search Cost for the Move-to-Root Rule with Random Weights.- Average-Case Analysis for the Probabilistic Bin Packing Problem.- Distribution of Wht Recurrences.- Probabilistic Analysis for Randomized Game Tree Evaluation.- Polynomial Time Perfect Sampling Algorithm for Two-Rowed Contingency Tables.- An Efficient Generic Algorithm for the Generation of Unlabelled Cycles.- Using Tries for Universal Data Compression.- IV. Trees.- New Strahler Numbers for Rooted Plane Trees.- An Average-Case Analysis of Basic Parameters of the Suffix Tree.- Arms and Feet Nodes Level Polynomial in Binary Search Trees.- Random Records and Cuttings in Complete Binary Trees.- Multidimensional Interval Trees.- Edit Distance between Unlabelled Ordered Trees.- Number of Vertices of a Given Outdegree in a Galton-Watson Forest.- Destruction of Recursive Trees.- V. Probability.- Restrictions on thePosition of the Maximum/Minimum in a Geometrically Distributed Sample.- Dual Random Fragmentation and Coagulation and an Application to the Genealogy of Yule Processes.- Semi-Markov Walks in Queueing and Risk Theory.- Representation of Fixed Points of a Smoothing Transformation.- Stochastic Fixed Points for the Maximum.- The Number of Descents in Samples of Geometric Random Variables.- Large Deviations for Cascades and Cascades of Large Deviations.- Partitioning with Piecewise Constant Eigenvectors.- Yaglom Type Limit Theorem for Branching Processes in Random Environment.- Two-Dimensional Limit Theorem for a Critical Catalytic Branching Random Walk.- VI. Combinatorial Stochastic Processes.- A Combinatorial Approach to Jumping Particles II: General Boundary Conditions.- Stochastic Deformations of Sample Paths of Random Walks and Exclusion Models.- A Markov Chain Algorithm for Eulerian Orientations of Planar Triangular Graphs.- Regenerative Composition Structures: Characterisation and Asymptotics of Block Counts.- Random Walks on Groups With a Tree-Like Cayley Graph.- Nested Regenerative Sets and Their Associated Fragmentation Process.- VII. Applications.- Real Numbers with Bounded Digit Averages.- Large Deviation Analysis of Space-Time Trellis Codes.- A Zero-One Law for First-Order Logic on Random Images.- Coarse and Sharp Transitions for Random Generalized Satisfyability Problems.- Stochastic Chemical Kinetics with Energy Parameters.- Large Deviations of Bellinger Distance on Partitions.- Estimation of the Offspring Mean for a General Class of Size-Dependent Branching Processes. Application to Quantitative Polymerase Chain Reaction.- A Constrained Version of Sauer's Lemma.- Author Index.
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