Higher Combinatorics

1. Front Matter

   Pages I-XIII

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2. Counting Theory

   1. Front Matter

      Pages 1-1

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   2. Enumeration of Partitions: The Role of Eulerian Series and q-Orthogonal Polynomials

      • George E. Andrews, Richard Askey

      Pages 3-26

   3. Distributions Euleriennes et Mahoniennes sur le Groupe des Permutations

      • Dominique Foata

      Pages 27-49

   4. Cohen-Macaulay Complexes

      • Richard P. Stanley

      Pages 51-62

3. Combinatorial Set Theory and Order Theory

   1. Front Matter

      Pages 63-63

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   2. Acyclic Orientations

      • Martin Aigner

      Pages 65-68

   3. Problems in Combinatorial Set Theory

      • Richard Rado

      Pages 69-78

   4. Aspects of Finite Lattices

      • R. Wille

      Pages 79-100

4. Matroids

   1. Front Matter

      Pages 101-101

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   2. Geometries Associated with Partially Ordered Sets

      • T. A. Dowling, W. A. Denig

      Pages 103-116

   3. Transversal Matroids and Related Structures

      • A. W. Ingleton

      Pages 117-131

   4. Matroids as the Study of Geometrical Configurations

      • J. H. Mason

      Pages 133-176

5. Designs

   1. Front Matter

      Pages 177-177

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   2. Partitions of X2 and Other Topics

      • Martin Aigner

      Pages 179-181

   3. Combinatorics of Partial Geometries and Generalized Quadrangles

      • J. A. Thas

      Pages 183-199

   4. Edge Decompositions of Colored Graphs

      • Martin Aigner

      Pages 201-202

6. Group and Coding Theory

   1. Front Matter

      Pages 203-203

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   2. Planes and Biplanes

      • E. F. Assmus Jr., Joseph A. Mezzaroba, Chester J. Salwach

      Pages 205-212

   3. Ovals from the Point of View of Coding Theory

      • E. F. Assmus Jr., Howard E. Sachar

      Pages 213-216

It is general consensus that Combinatorics has developed into a full-fledged mathematical discipline whose beginnings as a charming pastime have long since been left behind and whose great signifi­ cance for other branches of both pure and applied mathematics is only beginning to be realized. The last ten years have witnessed a tremendous outburst of activity both in relatively new fields such as Coding Theory and the Theory of Matroids as well as in' more time honored endeavors such as Generating Functions and the Inver­ sion Calculus. Although the number of text books on these subjects is slowly increasing, there is also a great need for up-to-date surveys of the main lines of research designed to aid the beginner and serve as a reference for the expert. It was the aim of the Advanced Study Institute "Higher Combinatorics" in Berlin, 1976, to help fulfill this need. There were five sections: I. Counting Theory, II. Combinatorial Set Theory and Order Theory, III. Matroids, IV. Designs and V. Groups and Coding Theory, with three principal lecturers in each section. Expanded versions of most lectures form the contents of this book. The Institute was designed to offer, especially to young researchers, a comprehen­ sive picture of the most interesting developments currently under way. It is hoped that these proceedings will serve the same purpose for a wider audience.

• Combinatorics
• Lattice
• Partition
• Permutation
• graphs

• Fachbereich Mathematik, Freie Universität Berlin, Berlin 33, Germany

  Martin Aigner

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