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]
Biographyedit
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]
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]
Bibliographyedit
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 publicationsedit
Booksedit
The Mathematical Gardner (editor), Publisher: Boston : Prindle, Weber & Schmidt; Belmont, Calif. : Wadsworth International, ISBN 0486400891, ISBN 9781468466867 (electronic book)[9]
Papersedit
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-densityJournal of Algorithms, Vol. 2, Issue 1, Pages 31–43, March 1981
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
^ abA 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
^ abKlarner systems and tiling boxes with polyominoes by Michael Reid, Journal of Combinatorial Theory, Series A, Vol. 111, Issue 1, July 2005, Pages 89-105
^A Finite Basis Theorem Revisited by David A. Klarner, Stanford University, Department of Computer Science, Report Number: CS-TR-73-338, February 1973
^ abcd"University of Calgary: Archives and Special Collections: David A. Klarner". Archived from the original on 2016-03-04. Retrieved 2017-08-06.
^ abGardner Tribute BooksThe 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."
^ ab
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.
^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
^ abAnother Fine Math You've Got Me Into. . ., By Ian Stewart, Dover Publications (January 15, 2004), p. 21, ISBN 0486431819
^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
^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."]
^Carl is a Political Scientist, receiving tenure at Indiana State University and currently working at the University of Florida as a research associate.
^Arithmetic properties of certain recursively defined sets by D. A. Klarner and R. Rado, Stanford University: Computer Science Department, March 1972
^Election Integrity, Past, Present and Future[permanent dead link] Caltech/MIT Voting Technology Project, Participants’ Biographies
^Fellowship Awards Offered National Science Foundation 1963
^"University of Nebraska-Lincoln Distinguished Teaching Awards: Past Recipients" (PDF). Archived from the original (PDF) on 2017-07-06. Retrieved 2017-08-08.
^David A. Klarner Fellowship for Computer Science University of Nebraska–Lincoln: Scholarships & Aid
^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.