David A. Klarner

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David Anthony Klarner (October 10, 1940 – March 20, 1999) was an American mathematician, author, and educator. He is known for his work in combinatorial enumeration, polyominoes,[1] and box-packing.[2][3][4]

Klarner was a friend and correspondent of mathematics popularizer Martin Gardner and frequently made contributions to Gardner's Mathematical Games column in Scientific American.[5] He edited a book honoring Gardner on the occasion of his 65th birthday.[6][7] Gardner in turn dedicated his twelfth collection of mathematical games columns to Klarner.[8]

Beginning in 1969 Klarner made significant contributions to the theory of combinatorial enumeration, especially focusing on polyominoes and box-packing.[9][3] Working with Ronald L. Rivest he found upper bounds on the number of n-omininoes.[2] Klarner's Theorem is the statement that an m by n rectangle can be packed with 1-by-x rectangles if and only if x divides one of m and n.[10][11]

He has also published important results in group theory[12] and number theory, in particular working on the Collatz conjecture (sometimes called the 3x + 1 problem).[13] The Klarner-Rado Sequence is named after Kleiner and Richard Rado.[14]

Biography

Klarner was born in Fort Bragg, California, and spent his childhood in Napa, California.[5]

He did his undergraduate work at Humboldt State College (1979-1980), got his Ph.D. at the University of Alberta in 1967, and did post-doctoral work at McMaster University in Hamilton, Ontario. He also did post-doctoral work at Eindhoven University of Technology in the Netherlands, and at the University of Reading in England. During his busy career he was at various times a visiting professor at Stanford University, at the State University of New York, at the University of Utrecht in the Netherlands, at the University of Waterloo in Ontario, and at Humboldt State College (1979-1980) in California. From 1981 to 1996 he was a professor of computer science at the University of Nebraska, at Lincoln. He retired to Eureka, California in 1996 and died there in 1999.[5]

Klarner was a frequent contributor to recreational mathematics and worked with many key mathematics popularizers including Ronald L. Rivest, Donald Coxeter, Ronald Graham, and Donald Knuth.[15][6]

He was a member of the Association of Computing Machinery, the American Mathematical Society, the Mathematical Association of America, and the Fibonacci Association.[5] He got a National Science Foundation Fellowship Award in mathematics in 1963.[16]

Bibliography

Selected publications

Books

  • The Mathematical Gardner (editor), Publisher: Boston : Prindle, Weber & Schmidt ; Belmont, Calif. : Wadsworth International, ISBN 0486400891, ISBN 9781468466867 (electronic book)[7]

Papers

References

  1. ↑ The Tromino Puzzle by Norton Starr
  2. ↑ 2.0 2.1 A procedure for improving the upper bound for the number of n-ominoes, by D. A. Klarner and R. L. Rivest, Can. J. Math., Vol. XXV, No. 3, 1973, pp. 5
  3. ↑ 3.0 3.1 Klarner systems and tiling boxes with polyominoes by Michael Reid, Journal of Combinatorial Theory, Series A, Vol. 111, Issue 1, July 2005, Pages 89-105
  4. ↑ A Finite Basis Theorem Revisited by David A. Klarner, Stanford University, Department of Computer Science, Report Number: CS-TR-73-338, February 1973
  5. ↑ 5.0 5.1 5.2 5.3 University of Calgary: Archives and Special Collections: David A. Klarner
  6. ↑ 6.0 6.1 Gardner Tribute Books The Mathematical Gardner, edited by David A. Klarner "It was quietly assembled behind the scenes, with the assistance of Ron Graham and Don Knuth, as a surprise for Martin to mark his announced retirement from his Scientific American column."
  7. ↑ 7.0 7.1 Reprinted in 1998 as Mathematical Recreations: A Collection in Honor of Martin Gardner (Dover; ISBN 0-486-40089-1), this book, edited by Klarner, was the tribute of the mathematical community to Gardner when he retired from writing his Scientific American column in 1981. Discreetly assembled for the occasion, the stature of the mathematicians submitting papers is a testament to Gardner's importance.
  8. ↑ A lifetime of puzzles : a collection of puzzles in honor of Martin Gardner's 90th birthday edited by Erik D Demaine, Martin L Demaine, and Tom Rodgers, Publisher: Wellesley, Massachusetts : A K Peters, Ltd. (2008), p. 346, ISBN 1568812450
  9. ↑ Packing a rectangle with congruent n-ominoes Journal of Combinatorial Theory, Vol. 7, Issue 2, September 1969, Pages 107-115
  10. ↑ Mathematical Gems Vol. 2, by Ross Honsberger The Mathematical Association of America: The Dolciani Mathematical Expositions, p. 88, 1976.
  11. ↑ Weisstein, Eric W., "Klarner's Theorem", MathWorld.
  12. ↑ A sufficient condition for certain semigroups to be free by David A Klarner, Journal of Algebra, Vol 74, Issue 1, January 1982, Pages 140-148
  13. ↑ Erdős, Klarner, and the 3x + 1 Problem by Jeffrey C. Lagarias, The American Mathematical Monthly, Vol. 123, No. 8, October 2016, pp. 753-776" [This paper describes work of Erdős, Klarner, and Rado on semigroups of integer affine maps and on sets of integers they generate. It gives the history of problems they studied, some solutions, and new unsolved problems that arose from them."]
  14. ↑ Klarner-Rado Sequence Michigan State University, MSU Librarie
  15. ↑ Election Integrity, Past, Present and Future Caltech/MIT Voting Technology Project, Participants’ Biographies
  16. ↑ Fellowship Awards Offered National Science Foundation 1963
  17. ↑ This is a 2016 revision by Barequet of the chapter of the same title originally written by Klarner for the first edition, and revised by Golomb for the second edition.

External links

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