Selected Publications

• Extinction probability for a critical general branching process, Stochastic Processes and Their Applications 2 (1974), 303-309.
• A generalization of Goldstein's comparison lemma and the exponential limit law in critical Crump-Mode-Jagers branching processes, Advances in Applied Probability 8 (1976), 88-104.
• Critical multitype branching processes, Annals of Probability 10 (1982), 482-495. MR 84a : 60103
• Prospects for computer use in foreign language education, The Review of Inquiry and Research, No. 43 (January 1986), Kansai University of Foreign Studies, 1-16.
• Chaos: The New Science: Nobel Conference XXVI, editor and author of introduction, University Press of America, Lanham, MD, 1993.
• The probability of n ace-king adjacencies in a shuffled deck, with Mark Holte, The Mathematical Gazette, Vol. 77, No. 480 (1993), 368-370.
• A Lucas-type theorem for fibonomial-coefficient residues, The Fibonacci Quarterly, Vol. 32, No. 1 (1994), 60-68. MR 94k #11023
• Carries, combinatorics, and an amazing matrix  (ps)  (pdf) The American Mathematical Monthly, Vol. 104, No. 2 (Feb. 1997), 138-149.
• Augmented amazing matrix, an uncut, earlier version, with additional results and proofs.
• Asymptotic prime-power divisibility of binomial, generalized binomial, and multinomial coefficients, Transactions of the American Mathematical Society, Vol. 349, No. 10 (Oct. 1997), 3837-3873.
• The probability that a queen sits beside a king: juxtapositions and runs in a random permutation, with Mark M. Holte and Kenneth A. Suman, The UMAP Journal, Vol. 19, No. 4 (Winter 1998), 373-394.
  Also in UMAP Modules 1998: Tools for Teaching, COMAP, 1999, Module 771, 109-130.
• Residues of generalized binomial coefficients modulo a prime, The Fibonacci Quarterly, Vol. 38, No. 3 (June-July 2000), 227-238.
• Fractal dimension of the arithmetical structure of generalized binomial coefficients modulo a prime, The Fibonacci Quarterly, Vol. 48, No. 1 (Feb 2006), 46-58.
  

Other Communications

• The probability a shuffled deck has no consecutive cards of equal rank, NCS-MAA meeting at Minot, 29 October 1994. (Problem 124.1 of M500 is solved by Bizley's binomial inversion formula.)
• When is f(1) + . . . + f(n) asymptotically of the same order as n f(n)? , NCS-MAA meeting at Carleton College, 17 April 1999: abstract.
• Fractal dimension of generalized binomial coefficients modulo a prime: preliminary report, Abstracts of the AMS, vol. 21, no. 1 (Jan. 2000) #950-11-950.
• Fractal dimension of generalized multinomial coefficients modulo a prime: preliminary report, Abstracts of the AMS (Jan. 2001) #962-11-890
  • Pictures
• Properties of O-regularly varying sequences: elementary proofs (ps) (pdf), International Congress of Mathematicians, Beijing 2002, August 20-28: Abstracts of Short Communications and Poster Sessions, Higher Education Press, Beijing, 2002, 393-394 (ps) (pdf).

Other Items

• A partition identity, Problem #1480, proposed by Ron Rietz and John Holte, Mathematics Magazine, Vol. 69, No. 4 (October 1996), 307.
• Book review: Chaos in the Cosmos: The Stunning Complexity of the Universe by Barry Parker, The Prairie Naturalist 28(4) (December 1996), 7-8.
• The Student Activities Zone, Focus 24:9 (December 2004), 12-13.