Mathematics and Computer Science III: Algorithms, Trees, Combinatorics and Probabilities: Trends in Mathematics

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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