Stationary Points at Infinity for Analytic Combinatorics

Analytic Combinatorics — Symbolic Combinatorics

This booklet develops in nearly 200 pages the basics of combinatorial enumeration through an approach that revolves around generating functions. The major objects of interest here are words, trees, graphs, and permutations, which surface recurrently in all areas of discrete mathematics. The text presents the core of the theory with chapters on unlabelled enumeration and ordinary generating func...

Analytic Combinatorics

The Order Steps of an Analytic Combinatorics

‎Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures‎. ‎This theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines‎, ‎including probability theory‎, ‎statistical physics‎, ‎computational biology and information theory‎. ‎With a caref...

Bundle Adjustment for Multi-camera Systems with Points at Infinity

We present a novel approach for a rigorous bundle adjustment for omnidirectional and multi-view cameras, which enables an efficient maximum-likelihood estimation with image and scene points at infinity. Multi-camera systems are used to increase the resolution, to combine cameras with different spectral sensitivities (Z/I DMC, Vexcel Ultracam) or – like omnidirectional cameras – to augment the e...

Analytic Combinatorics of Non-crossing Conngurations Analytic Combinatorics of Non-crossing Conngurations Analytic Combinatorics of Non-crossing Conngurations

This paper describes a systematic approach to the enumeration of \non-crossing" geometric conngurations built on vertices of a convex n-gon in the plane. It relies on generating functions, symbolic methods, singularity analysis, and singularity perturbation. A consequence is exact and asymptotic counting results for trees, forests, graphs, connected graphs, dissections, and partitions. Limit la...