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9062 results in Discrete Mathematics, Information Theory and Coding

Page 368 of 454

  • Preface

  • Richard A. Brualdi, University of Wisconsin, Madison, Herbert J. Ryser, California Institute of Technology
  • Book:
    Combinatorial Matrix Theory
    Published online:
    05 May 2013
    Print publication:
    26 July 1991, pp vii-x

  • Summary

    It was on March 20, 1984, that I wrote to Herb Ryser and proposed that we write together a book on the subject of combinatorial matrix theory. He wrote back nine days later that “I am greatly intrigued by the idea of writing a joint book with you on combinatorial matrix theory. … Ideally, such a book would contain lots of information but not be cluttered with detail. Above all it should reveal the great power and beauty of matrix theory in combinatorial settings. … I do believe that we could come up with a really exciting and elegant book that could have a great deal of impact. Let me say once again that at this time I am greatly intrigued by the whole idea.” We met that summer at the small Combinatorial Matrix Theory Workshop held in Opinicon (Ontario, Canada) and had some discussions about what might go into the book, its style, a timetable for completing it, and so forth. In the next year we discussed our ideas somewhat more and exchanged some preliminary material for the book. We also made plans for me to come out to Caltech in January, 1986, for six months in order that we could really work on the book. Those were exciting days filled with enthusiasm and great anticipation.

    Herb Ryser died on July 12, 1985. His death was a big loss for me. Strange as it may sound, I was angry. Angry because Herb was greatly looking forward to his imminent retirement from Caltech and to our working together on the book. In spite of his death and as previously arranged, I went to Caltech in January of 1986 and did some work on the book, writing preliminary versions of what are now Chapters 1, 2, 3, 4, 5 and 6. As I have been writing these last couple of years, it has become clear that the book we had envisioned, a book of about 300 pages covering the basic results and methods of combinatorial matrix theory, was not realistic.

  • MTK volume 38 issue 1 Cover and Front matter

  • Journal:
    Mathematika / Volume 38 / Issue 1 / June 1991
    Published online by Cambridge University Press:
    26 February 2010, pp. f1-f4
    Print publication:
    June 1991
    • Article
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  • A note on radial variation of analytic functions

  • D. J. Hallenbeck, K. Samotij
  • Journal:
    Mathematika / Volume 38 / Issue 1 / June 1991
    Published online by Cambridge University Press:
    26 February 2010, pp. 191-193
    Print publication:
    June 1991

  • Let F denote a family of analytic functions in the unit disk Δ. Suppose that one has a “sharp” estimate on the almost everywhere radial variation of functions in the class Δ. We prove that if Δ is contained in the Nevanlinna class N then the estimate will be “sharp” in the algebra A of functions analytic in Δ and continuous in Δ.

  • On the number of integral ideals of given norm and ray-class

  • Part of
  • R. W. K. Odoni
  • Journal:
    Mathematika / Volume 38 / Issue 1 / June 1991
    Published online by Cambridge University Press:
    26 February 2010, pp. 185-190
    Print publication:
    June 1991

  • Let K be an algebraic number field, [K: Q] = κ є N; only the case κ > 1 is of interest in this paper. Let f be any non-zero ideal in ZK, the ring of integers of K, and let b be any ray-class (modx f) of K. In this paper we answer a question of P. Erdös (private communication) about the “maximum-growth-rate” of the functions

    and

    the sum here taken over all ray-classes (modx f), while N(a) is the absolute norm of a. Let

    and

    where, as usual, for x є R, log+ x - log max {1, x}. We prove

    THEOREM 1. For every f, b we have

Page 368 of 454