LOGARITHMIC COMBINATORIAL STRUCTURES

RICHARD ARRATIA; A. D. BARBOUR; SIMON TAVARE

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LOGARITHMIC COMBINATORIAL STRUCTURES

by RICHARD ARRATIA; A. D. BARBOUR; SIMON TAVARE

EUROPEAN MATHEMATICAL SOC.

1

9783037195000

3037195002

Description

The elements of many classical combinatorial structures can be naturally decomposed into components. Permutations can be decomposed into cycles, polynomials over a finite field into irreducible factors, mappings into connected components. In all of these examples, and in many more, there are strong similarities between the numbers of components of different sizes that are found in the decompositions of `typical' elements of large size. For instance, the total number of components grows logarithmically with the size of the element, and the size of the largest component is an appreciable fraction of the whole. This book explains the similarities in asymptotic behaviour as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient. The book is thus of particular interest to graduate students and researchers in both combinatorics and probability theory.

Frequently Asked Questions

How many pages are in LOGARITHMIC COMBINATORIAL STRUCTURES?

This edition of LOGARITHMIC COMBINATORIAL STRUCTURES has approximately 1 pages. Please note, this is an estimate and the exact page count can vary between hardcover, paperback, and e-book versions.

How long does it take to read LOGARITHMIC COMBINATORIAL STRUCTURES?

For most readers, LOGARITHMIC COMBINATORIAL STRUCTURES typically takes between 1m and 1m to complete. This is based on the book's length of approximately 250 words and common reading speeds.

Here's a detailed breakdown: • Continuous reading at 250 WPM: approximately 1m of focused reading • Casual reading (30 minutes/day): you could finish in roughly 1 day • Estimated word count: 250 words

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What is the word count of LOGARITHMIC COMBINATORIAL STRUCTURES?

The estimated word count for LOGARITHMIC COMBINATORIAL STRUCTURES is approximately 250 words. This figure is calculated using industry-standard methods that consider genre-specific word density patterns, typical formatting and layout characteristics, and standard words-per-page ratios for published books.

This is an approximation — actual word count may vary based on font size, formatting, edition, and the presence of illustrations or charts.

Who is the author of LOGARITHMIC COMBINATORIAL STRUCTURES?

LOGARITHMIC COMBINATORIAL STRUCTURES was written by RICHARD ARRATIA; A. D. BARBOUR; SIMON TAVARE.