David A. Klarner Explained

David A. Klarner
Birth Name:David Anthony Klarner
Birth Date:10 October 1940
Birth Place:Fort Bragg, California
Nationality:American
Death Place:Eureka, California
Field:Mathematics
Work Institutions:University of Calgary
Alma Mater:University of Alberta
Doctoral Advisor:John W. Moon
Doctoral Students:Jean Scholtz
Thesis Title:On some combinatorial and probabilistic aspects of bipartite graphs
Known For:Combinatorics
Klarner's Theorem
Klarner-Rado Sequence
Recreational mathematics

David Anthony Klarner (October 10, 1940March 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]

Klarner was a friend and correspondent of mathematics popularizer Martin Gardner and frequently made contributions to Gardner's Mathematical Games column in Scientific American. He edited a book honoring Gardner on the occasion of his 65th birthday.[4] Gardner in turn dedicated his twelfth collection of mathematical games columns to Klarner.[5]

Beginning in 1969 Klarner made significant contributions to the theory of combinatorial enumeration, especially focusing on polyominoes[6] and box-packing.[7] [8] Working with Ronald L. Rivest he found upper bounds on the number of n-ominoes.[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.[9]

He has also published important results in group theory[10] and number theory, in particular working on the Collatz conjecture (sometimes called the 3x + 1 problem).[11] The Klarner-Rado Sequence is named after Klarner and Richard Rado.[12]

Biography

Klarner was born in Fort Bragg, California, and spent his childhood in Napa, California.[13] He married Kara Lynn Klarner in 1961. Their son Carl Eoin Klarner was born on April 21, 1969.[14]

Klarner did his undergraduate work at Humboldt State University (1960–63), got his Ph.D. at the University of Alberta (1963–66), and did post-doctoral work at McMaster University in Hamilton, Ontario (1966–68). He also did post-doctoral work at Eindhoven University of Technology in the Netherlands (1968-1970), at the University of Reading in England working with Richard Rado (1970–71),[15] and at Stanford University (1971–73). He served as an assistant professor at Binghamton University (1973–79) and was a visiting professor at Humboldt State University in California (1979–80). He returned to Eindhoven as a professor (1980–81), and to Binghamton (1981–82). From 1982 to 1996 he was a professor of computer science at the University of Nebraska, at Lincoln, with a one-year break at Eindhoven in academic year 1991–92. He retired to Eureka, California in 1997 and died there in 1999.[13]

He was a frequent contributor to recreational mathematics and worked with many key mathematics popularizers including Ronald L. Rivest, John H. Conway, Richard K. Guy, Donald Coxeter, Ronald Graham, and Donald Knuth.[16] [4] [17] [6]

Organizations and awards

Klarner was a member of the Association for Computing Machinery, the American Mathematical Society, the Mathematical Association of America, and the Fibonacci Association.[13] He was awarded a National Science Foundation Fellowship Award in mathematics in 1963.[18] In 1986 Klarner received a University of Nebraska-Lincoln Distinguished Teaching Award in Computer Science.[19]

The David A. Klarner Fellowship for Computer Science was set up after Klarner's death by Spyros Magliveras a fellow professor in Computer Science at UNL.[20]

Bibliography

Selected publications

Books

Papers

External links

Notes and References

  1. The Tromino Puzzle by Norton Starr
  2. https://people.csail.mit.edu/rivest/pubs/KR73.pdf A procedure for improving the upper bound for the number of n-ominoes
  3. http://i.stanford.edu/pub/cstr/reports/cs/tr/73/338/CS-TR-73-338.pdf A Finite Basis Theorem Revisited
  4. 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."
  5. 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,
  6. Another Fine Math You've Got Me Into. . ., By Ian Stewart, Dover Publications (January 15, 2004), p. 21,
  7. Packing a rectangle with congruent n-ominoes Journal of Combinatorial Theory, Vol. 7, Issue 2, September 1969, Pages 107-115
  8. 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
  9. Mathematical Gems Vol. 2, by Ross Honsberger The Mathematical Association of America: The Dolciani Mathematical Expositions, p. 88, 1976.
  10. 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
  11. 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."]
  12. https://archive.lib.msu.edu/crcmath/math/math/k/k083.htm Klarner-Rado Sequence
  13. Web site: University of Calgary: Archives and Special Collections: David A. Klarner . 2017-08-06 . 2016-03-04 . https://web.archive.org/web/20160304203637/https://asc.ucalgary.ca/node/83 . dead .
  14. Carl is a Political Scientist, receiving tenure at Indiana State University and currently working at the University of Florida as a research associate.
  15. Arithmetic properties of certain recursively defined sets by D. A. Klarner and R. Rado, Stanford University: Computer Science Department, March 1972
  16. Election Integrity, Past, Present and Future Caltech/MIT Voting Technology Project, Participants’ Biographies
  17. The Penrose Tiling at Miami University by David Kullman, Presented at the Mathematical Association of America Ohio Section Meeting Shawnee State University, October 24, 1997
  18. https://www.nsf.gov/pubs/1963/annualreports/ar_1963_appendix_e.pdf Fellowship Awards Offered
  19. Web site: University of Nebraska-Lincoln Distinguished Teaching Awards: Past Recipients . 2017-08-08 . 2017-07-06 . https://web.archive.org/web/20170706222058/http://academicaffairs.unl.edu/documents/CDTA-past-recipients.pdf . dead .
  20. http://cse.unl.edu/scholarships David A. Klarner Fellowship for Computer Science
  21. Reprinted in 1998 as Mathematical Recreations: A Collection in Honor of Martin Gardner (Dover;), 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.
  22. 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.

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