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]
David A. Klarner | |
|---|---|
| Born | David Anthony Klarner October 10, 1940 |
| Died | March 20, 1999 (aged 58) |
| Nationality | American |
| Alma mater | University of Alberta |
| Known for | Combinatorics Klarner's Theorem[1] Klarner-Rado Sequence[2] Recreational mathematics |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Calgary |
| Thesis | On some combinatorial and probabilistic aspects of bipartite graphs |
| Doctoral advisor | John W. Moon |
| Doctoral students | Jean Scholtz |
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]
Biography
Klarner was born in Fort Bragg, California, and spent his childhood in Napa, California.[7] He married Kara Lynn Klarner in 1961. Their son Carl Eoin Klarner was born on April 21, 1969.[16]
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),[17] 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.[7]
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.[18][8][19][11]
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.[7] He was awarded a National Science Foundation Fellowship Award in mathematics in 1963.[20] In 1986 Klarner received a University of Nebraska-Lincoln Distinguished Teaching Award in Computer Science.[21]
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.[22]
Bibliography
- Asymptotically Optimal Box Packing Theorems: Klarner systems by Michael Reid, Department of Mathematics, University of Central Florida, June, 2008
- A Lifetime of Puzzles edited by Erik D. Demaine, Martin L. Demaine, Tom Rodgers; pp. 221–225: Satterfield's Tomb, a puzzle by David A. Klarner and Wade Satterfield; ISBN 1568812450
Selected publications
Books
- The Mathematical Gardner (editor), Publisher:Boston : Prindle, Weber & Schmidt; Belmont, Calif. : Wadsworth International, ISBN 0486400891, ISBN 9781468466867 (electronic book)[9]
Papers
- Polyominoes by Gill Barequet, Solomon W. Golomb, and David A. Klarner, December 2016[23]
- The number of tilings of a block with blocks (with F. S. S. Magliveras), European Journal of Combinatorics: Volume 9 Issue 4, July 1988
- The number of tiered posets modulo six[permanent dead link] Discrete Mathematics, Vol. 62, Issue 3, pp. 295–297, December 1986
- Asymptotics for coefficients of algebraic functions (with Patricia Woodworth), Aequationes Mathematicae, Volume 23, Issue 1, pp. 236–241, December 1981
- An algorithm to determine when certain sets have 0-density Journal of Algorithms, Vol. 2, Issue 1, Pages 31–43, March 1981
- Some remarks on the Cayley-Hamilton theorem American Mathematical Monthly, Vol. 83, No. 5, pp. 367–369, May, 1976
- Asymptotic bounds for the number of convex n-ominoes[permanent dead link] (with Ronald L. Rivest), Discrete Mathematics, Vol. 8, Issue 1, pp. 31–40, March 1974
- A finite basis theorem revisited[permanent dead link] Stanford University: Computer Science Department, April 1973
- The number of SDR's in certain regular systems Stanford University: Computer Science Department, April 1973
- Selected combinatorial research problems (with Václav Chvátal and Donald E. Knuth), Stanford University: Computer Science Department, June 1972
- Sets generated by iteration of a linear operation Stanford University: Computer Science Department, March 1972
- Linear Combinations of Sets of Consecutive Integers (with Richard Rado), Stanford University: Computer Science Department, March 1972
- Sets generated by iteration of a linear operation Stanford University: Computer Science Department, March 1972
- Packing a rectangle with congruent n-ominoes Journal of Combinatorial Theory, Vol. 7, Issue 2, Pages 107–115, September 1969
- Packing boxes with congruent figures (with F. Göbel), Indagationes Mathematicae 31, pp. 465–472, MR 40 #6362, 1969
- Some Results Concerning Polyominoes Fibonacci Quarterly, 3, pp. 9–20, February 1965
References
External links
- David A. Klarner at the Mathematics Genealogy Project
- David A. Klarner fonds University of Calgary Special Collections