Surveys in combinatorics 2024 / edited by Felix Fischer, Robert Johnson.

Format:

Book

Contributor:

Fischer, Felix (Mathematician), editor.

Johnson, Robert (Mathematician), editor.

Series:

London Mathematical Society lecture note series ; 493.

London Mathematical Society lecture note series ; 493

Language:

English

Subjects (All):

Combinatorial analysis.

Physical Description:

1 online resource (vii, 295 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2024.

Summary:

This volume contains nine survey articles by the invited speakers of the 30th British Combinatorial Conference, one of the major international events in combinatorics. Written by leading experts in the field, these articles provide a snapshot of current developments in combinatorics for researchers and graduate students in discrete mathematics

Contents:

Cover

Half-title page

Title page

Copyright page

Contents

Preface

1 Intersection Theory of Matroids: Variations on a Theme

1 Introduction

1.1 Theme

2 Intersection Theory of Toric Varieties: A Case Study

2.0 The Braid Fan

2.1 The Chow Ring as a Quotient of a Polynomial Ring

2.2 The Chow Ring in Terms of Piecewise Polynomials

2.3 The Chow Ring in Terms of Minkowski Weights

2.4 The Chow Ring in Terms of Tropical Intersection

2.5 Morphisms

2.6 Geometry: The Cohomology and Chow Ring of a Toric Variety

3 Intersection Theory of Matroids: Four Approaches

3.0 Matroids, Characteristic Polynomials, and Matroid Fans

3.1 The Chow Ring as a Quotient of a Polynomial Ring

3.2 The Chow Ring in Terms of Piecewise Polynomials

3.3 The Chow Ring in Terms of Minkowski Weights

3.4 The Chow Ring in Terms of Tropical Intersection

4 Further Developments

Acknowledgements

References

2 Erdős Covering Systems

2 Minimum Modulus and the Density of the Uncovered Set

3 Divisibility Constraints

4 Counting Covering Systems

5 The Distortion Method

4.3 Triangle-Free Graphs

4.4 Further Applications of Cluster Expansion and Counting

5 The Algorithmic Perspective

5.1 Barvinok's Interpolation Method

5.2 Algorithmic Applications of the Cluster Expansion

4 Sublinear Expanders and Their Applications

2 Subdivisions

2.1 Finding Clique Subdivisions

2.2 Clique Subdivisions in C4-Free Graphs

2.3 Crux and Clique Subdivisions

2.4 Subdivisions of Sparse Graphs

3 Small Minors and Subdivisions

3.1 Almost Logarithmically Small Clique Minors

3.2 Logarithmically Small Clique Minors and Subdivisions

4 Immersions

4.1 Clique Immersions in K[sub(s,t)]-Free Graphs

4.2 Immersions in Directed Graphs

5 The Odd Cycle Problem and Balanced Subdivisions

5.1 Cycle Lengths in Graphs With Large Average Degree

5.2 Improved Bounds on Average Degree Implying Balanced Clique Subdivision

6 Tight Cycles, Rainbow Subdivisions, and Cycles With Many Chords

6.1 Hypergraphs With No Tight Cycles

6.2 Rainbow Clique Subdivisions

6.3 Cycles With Many Chords

6.4 A Sampling Trick

Notes:

Title from publisher's bibliographic system (viewed on 28 May 2024).

ISBN:

9781009490542

1009490540

9781009490559

1009490559