David A. Klarner

David A. Klarner

{{Infobox scientist | name = David A. Klarner | birth_name = David Anthony Klarner | image = | caption = Left to Right: David Klarner, George Pólya, Nicolaas Govert de Bruijn in March 1973 | image_size = 250px | birth_date = | birth_place = Fort Bragg, California | residence = | death_date = | death_place = Eureka, California | field = Mathematics | work_institutions = University of Calgary | alma_mater = University of Alberta | doctoral_advisor = John W. Moon | doctoral_students = | thesis_title = On some combinatorial and probabilistic aspects of bipartite graphs | thesis_url = | thesis_year = | known_for = CombinatoricsKlarner's Theorem and box-packing.

Klarner was a friend and correspondent of mathematics popularizer Martin Gardner and frequently made contributions to Gardner's Mathematical Games column in Scientific American.

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

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

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

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), 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–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. In 1986 Klarner received a University of Nebraska-Lincoln Distinguished Teaching Award in Computer Science.

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.

Bibliography Asymptotically Optimal Box Packing Theorems: Klarner systems* by Michael Reid, Department of Mathematics, University of Central Florida, June, 2008 [A Lifetime of Puzzles](https://books.google.com/books?id=cU3NBQAAQBAJ&dq=klarner+thane&pg=PA221) 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;

Selected publications ### Books The Mathematical Gardner* (editor), Publisher: Boston : Prindle, Weber & Schmidt; Belmont, Calif. : Wadsworth International, , (electronic book)

Papers Polyominoes* by Gill Barequet, [[solomon-w.-golomb]], and David A. Klarner, December 2016 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 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 (with Ronald L. Rivest), Discrete Mathematics*, Vol. 8, Issue 1, pp. 31–40, March 1974 A finite basis theorem revisited* 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 fonds](https://searcharchives.ucalgary.ca/uploads/r/university-of-calgary-special-collections/0/7/6/07647bdbd77a4c7158a698a69ba44d86d9ee1e0578b3473febe9eefea5bf6d2e/F0193_Klarner__David_A.pdf) University of Calgary Special Collections