David A. Klarner

David A. Klarner
Born
David Anthony Klarner

(1940-10-10)October 10, 1940
Fort Bragg, California
DiedMarch 20, 1999(1999-03-20) (aged 58)
Eureka, California
NationalityAmerican
Alma materUniversity of Alberta
Known forCombinatorics
Klarner's Theorem[1]
Klarner-Rado Sequence[2]
Recreational mathematics
Scientific career
FieldsMathematics
InstitutionsUniversity of Calgary
Thesis On some combinatorial and probabilistic aspects of bipartite graphs
Doctoral advisorJohn W. Moon
Doctoral studentsJean Scholtz

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,[3] and box-packing.[4][5][6]

Klarner was a friend and correspondent of mathematics popularizer Martin Gardner and frequently made contributions to Gardner's Mathematical Games column in Scientific American.[7] He edited a book honoring Gardner on the occasion of his 65th birthday.[8][9] Gardner in turn dedicated his twelfth collection of mathematical games columns to Klarner.[10]

Beginning in 1969 Klarner made significant contributions to the theory of combinatorial enumeration, especially focusing on polyominoes[11] and box-packing.[12][5] Working with Ronald L. Rivest he found upper bounds on the number of n-ominoes.[4] 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.[1][13]

He has also published important results in group theory[14] and number theory, in particular working on the Collatz conjecture (sometimes called the 3x + 1 problem).[15] The Klarner-Rado Sequence is named after Klarner and Richard Rado.[2]

  1. ^ a b Mathematical Gems Vol. 2, by Ross Honsberger The Mathematical Association of America: The Dolciani Mathematical Expositions, p. 88, 1976.
  2. ^ a b Klarner-Rado Sequence Michigan State University, MSU Librarie
  3. ^ The Tromino Puzzle by Norton Starr
  4. ^ a b 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
  5. ^ a b 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
  6. ^ A Finite Basis Theorem Revisited by David A. Klarner, Stanford University, Department of Computer Science, Report Number: CS-TR-73-338, February 1973
  7. ^ Cite error: The named reference calgary was invoked but never defined (see the help page).
  8. ^ 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."
  9. ^ Cite error: The named reference gardner was invoked but never defined (see the help page).
  10. ^ 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
  11. ^ Another Fine Math You've Got Me Into. . ., By Ian Stewart, Dover Publications (January 15, 2004), p. 21, ISBN 0486431819
  12. ^ Packing a rectangle with congruent n-ominoes Journal of Combinatorial Theory, Vol. 7, Issue 2, September 1969, Pages 107-115
  13. ^ Weisstein, Eric W. "Klarner's Theorem". MathWorld.
  14. ^ 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
  15. ^ 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."]