Publications of Joseph Arkin

 

  1. Arkin, Joseph, Congruences for the coefficients of the k-th power of a power series. The American Mathematical Monthly, 71, 1964, 899-900. (MR29 #5793 review by L. Carlitz) 10.06.    

  2. Arkin, Joseph, An extension of the Fibonacci numbers. The American Mathematical Monthly, 72, 1965, 275-279. (MR31 #2194 review by L. K. Durst) 10.61.

  3. Arkin, Joseph, Congruences for the coefficients of the k-th power of a power series. II. The American Mathematical Monthly, 72, 1965, 390-393. (MR 31 #4753 review by L. Carlitz) 10.06.

  4. Arkin, Joseph, A function whose values are integers. Mathematics Magazine, 38, 1965, 196-199. 10.05. MR31 #4751.

  5. Arkin, Joseph, An extension of a theorem of Ramanujan. The American Mathematical Monthly, 73, 1966, 1087-1090. (MR 34 #4187 review by B. M. Stewart) 10.05 (10.06).

  6. Arkin, Joseph, A note on a theorem of Jacobi. The Fibonacci Quarterly, 4, 1966, 359-362. (MR 37 #140 review by P. Erdös) 10.07.

  7. Arkin, Joseph, Convergence of the coefficients in a recurring power series. The Fibonacci Quarterly, 7, 1969, 41-55. (MR 39 #3183 review by A. L. Whiteman) 40.20.

  8. Arkin, Joseph; Pollack, Richard Recurrence formulas. The Fibonacci Quarterly, 8, 1970, no. 1, 4-5. 10.48. MR 41 #1669.

  9. Arkin, Joseph; Hoggatt, Verner E., Jr. An extension of the Fibonacci numbers. II. The Fibonacci Quarterly, 8, 1970, no. 2, 199-216. (MR 41 #3382 review by D. A. Klarner) 10.09.

  10. Arkin, Joseph, Researches on partitions. Duke Mathematical Journal, 37, 1970, 403-409. (MR 42 #5897 review by H. Gupta) 10.07.

  11. Proceedings of the Washington State University Conference on Number Theory (Washington State Univ., Pullman, Wash., 24-27 March 1971). Edited by James H. Jordan and William A. Webb. Department of Mathematics; Pi Mu Epsilon, Washington State University, Pullman, Wash., 1971. vii+228 pp. 10-00 (00A10). MR 47 #4904.

  12. Arkin, Joseph, Researches on some classical problems. Proceedings of the Washington State University Conference on Number Theory (Pullman, Wash., 1971), pp. 130-147. Dept. Math., Washington State Univ., Pullman, Wash., 1971. (MR 47 #6637 review by George E. Andrews) 10J2.

  13. Arkin, Joseph; Arney, David C.; Porter, Bruce J., A Perfect 4-Dimensional Hypercube of Order 7 – “The Cameron Cube", Journal of Recreational Mathematics, 21 (1989), no. 2, 81-88.

  14. Arkin, Joseph, The first solution of the classical Eulerian magic cube problem of order ten. The Fibonacci Quarterly, 11 (1973), no. 2, 174-178. (MR 47 #3199 review by J. Schonheim) 05B15.

  15. Arkin, Joseph, Convergence of the coefficients in the k\sp{th} power of a power series. The Fibonacci Quarterly, 11 (1973), no. 1, 15-24. (MR 47 #8416 review by R. N. Jain) 10A35.

  16. Arkin, Joseph; Hoggatt, V. E., Jr., The Arkin-Hoggatt Game and the Solution of a Classical Problem, Journal of Recreational Mathematics, 6 (1973), no. 2, 120-121.

  17. Arkin, Joseph, A solution to the classical problem of finding systems of three mutually orthogonal numbers in a cube formed by three superimposed 10\times 10\times 10 cubes. The Fibonacci Quarterly, 11 (1973), no. 5, 485-489, 494. (MR 50 #1922 review by H. Hanani) 05B15.

  18. Arkin, Joseph; Hoggatt, V. E., Jr. Exploded myths. Journal of Recreational Mathematics, 7 (1974), no. 2, 90-94. (MR 56 #8396 review by K. Yamamoto) 05B15.

  19. Arkin, Joseph, A solution of orthogonal triples in four superimposed 10\times 10\times 10 Latin Cubes. The Fibonacci Quarterly, 12 (1974), 133-140. (MR 51 #7904 review by David A. Drake) 05B15.

  20. Arkin, Joseph; Straus, E. G. Latin k-cubes. The Fibonacci Quarterly, 12 (1974), 288-292. (MR 50 #4337 review by David A. Drake) 05B15.

  21. Arkin, Joseph; Hoggatt, V. E., Jr. The generalized Fibonacci number and its relation to Wilson's theorem. The Fibonacci Quarterly, 13 (1975), 107-110. (MR 50 #12900 review by S. A. Burr) 10A40.

  22. Arkin, Joseph; Smith, Paul Trebly-magic systems in a Latin 3-cube of order eight. The Fibonacci Quarterly, 14 (1976), no. 2, 167-170. (MR 53 #12985 review by Bhagwandas) 05B15.

  23. Arkin, Joseph; Hoggatt, Verner E., Jr.; Straus, E. G. Systems of magic Latin k-cubes. Canadian Mathematical Journal,  28 (1976), no. 6, 1153-1161. (MR 54 #12541 review by Heiko Harborth) 05B15.

  24. Arkin, Joseph; Hoggatt, V. E., Jr.; Straus, E. G. On Euler's solution of a problem of Diophantus. The Fibonacci Quarterly, 17 (1979), no. 4, 333-339. (MR 80m:10009 review by Maurice Craig) 10B05.

  25. Arkin, Joseph; Hoggatt, V. E., Jr.; Straus, E. G. On Euler's solution to a problem of Diophantus. II. The Fibonacci Quarterly, 18 (1980), no. 2, 170-176. (MR 82b:10015 review by Maurice Craig) 10B05.

  26. Arkin, Joseph; Singh, K. A new type magic Latin 3-cube of order ten. The Fibonacci Quarterly, 19 (1981), no. 1, 76-82. 05B15. MR 82d:05032

  27. Arkin, Joseph; Straus, E. G. Orthogonal Latin systems. The Fibonacci Quarterly, 19 (1981), no. 4, 289-293. (MR 82m:05033 review by R. C. Mullin) 05B99 (05B15).

  28. Arkin, Joseph; Smith, Paul; Straus, E. G. Euler's 36 officers problem in three dimensions--solved. Journal of Recreational Mathematics, 15 (1982/83), no. 2, 81-84. (MR 84e:05032 review by A. E. Brouwer) 05B15.

  29. Arkin, Joseph, An extension of E. G. Straus' perfect Latin 3-cube of order 7. Pacific Journal of  Mathematics, 118 (1985), no. 2, 277-280. (MR 86j:05037 review by G. H. J. Van Rees) 05B15.

  30. Arkin, Joseph; Bergum, Gerald,  More on the problem of Diophantus. Applications of Fibonacci numbers (San Jose, CA, 1986), 177-181, Kluwer Acad. Publ., Dordrecht, 1988. (MR 89f:11010 review by Md. Fazlee Hossain) 11A05.

  31. Arkin, Joseph; Arney, David C.; Bergum, Gerald E.; Burr, Stefan A.; Porter, Bruce J. Unique Fibonacci formulas. The Fibonacci Quarterly, 27 (1989), no. 4, 296-302. (MR 90i:05007 review by Louis Shapiro) 05A19. 

  32. Arkin, Joseph; Arney, David C.; Bergum, Gerald E.; Burr, Stefan A.; Porter, Bruce J. Recurring-sequence tiling. The Fibonacci Quarterly, 27 (1989), no. 4, 323-332. (MR 90g:05064 review by Louis Shapiro) 05B45 (11B39). 

  33. Arkin, Joseph; Arney, David C.; Bergum, Gerald E.; Burr, Stefan A.; Porter, Bruce J. Tiling the k-th power of a power series. The Fibonacci Quarterly, 28 (1990), no. 3, 266-272. 11B37 (05B45 58F40). MR91h:11010.

  34. Arkin, Joseph; Arney, David C.; Dewald, Lee S.; Kennedy, Charles Applications of Fibonacci sequences and tiling. Transactions of the Seventh Army Conference on Applied Mathematics and Computing (West Point, NY, 1989), 743-763, ARO Rep., 90-1, U.S. Army Res. Office, Research Triangle Park, NC, 1990. (MR91g:11013 review by John Christopher Turner) 11B39 (05B40 52C20). 

  35. Arkin, Joseph; Arney, David C.; Dewald, Lee S.; Giordano, Frank R. Supercube. Applications of Fibonacci numbers, Vol. 4 (Winston-Salem, NC, 1990), 17-32, Kluwer Acad. Publ., Dordrecht, 1991. 05B15. Listed MR  1 193 696.

  36. Arkin, Joseph; Arney, David C.; Giordano, Frank R.; Kolb, Rickey A. A note on fundamental properties of recurring series. Applications of Fibonacci numbers, Vol. 4 (Winston-Salem, NC, 1990), 33-36, Kluwer Acad. Publ., Dordrecht, 1991. (MR93m:11004 review by Ronald J. Evans) 11A07 (11B65). 

  37. Arkin, Joseph; Arney, David C.; Luchins, Edith H. A function whose values are integers. II. Transactions of the Tenth Army Conference on Applied Mathematics and Computing (West Point, NY, 1992), 87-90, ARO Rep., 93-1, U.S. Army Res. Office, Research Triangle Park, NC, 1993. (MR94h:11019 review by Bruce C. Berndt) 11B99. 

  38. Arkin, Joseph; Arney, David C.; Giordano, Frank R.; Kolb, Rickey A.; Smith, Paul Reverse digit constructions of perfect, magic, and doubly magic cubes. Transactions of the Tenth Army Conference on Applied Mathematics and Computing (West Point, NY, 1992), 91-101, ARO Rep., 93-1, U.S. Army Res. Office, Research Triangle Park, NC, 1993. 05B15. Listed MR  1 224 060.

  39. Arkin, Joseph; Arney, David C.; Giordano, Frank R.; Kolb, Rickey A.; Bergum, Gerald E. An extension of an old classical Diophantine problem. Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 45-48, Kluwer Acad. Publ., Dordrecht, 1993. (MR95c:11041 review by Nikos Tzanakis) 11D99 (11B39). 

  40. Arkin, Joseph; Arney, David C.; Kolb, Rickey A. Generating primes using tables of the generalized Fibonacci power series. Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994). Congr. Numer. 101 (1994), 27-31. (MR96m:11118 review by Pentti Haukkanen) 11Y11 (11A51 11B39). 

  41. Arkin, Joseph; Arney, David C. Latin k-cubes with special properties. Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995). Congr. Numer. 112 (1995), 129-150. 05B15. Listed MR 1 369 370.

  42. Arkin, Judith L.; Arkin, Joseph, A privately taped interview with Paul Erdös. Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995). Congr. Numer. 112 (1995), 208-212. 01A70. Listed MR  1 369 377.

  43. Arkin, Joseph; Arney, David C. Arkin-Smith's unique constructions on pairs of certain orthogonal Latin squares of even order. Proceedings of the Twenty-seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 1996). Congr. Numer. 118 (1996), 127-128. 05B15. Listed MR  1 431 919.

  44. Arkin, Joseph; Arney, David C.; Erdos, Paul Two theorems of Arkin-Arney-Erdos. Proceedings of the Twenty-seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 1996). Congr. Numer. 119 (1996), 151-159. 11A07. Listed MR 1 431 944.

  45. Arkin, Joseph; Arney, David C. Researches on partitions, revisited. Proceedings of the Twenty-eighth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1997). Congr. Numer. 127 (1997), 107-115. 05A17. MR98j:05013.

  46. Arkin, Joseph; Smith, Paul The Arkin-Smith construction on pairs of orthogonal Latin squares of order 14. Edited by Arkin and David C. Arney. Proceedings of the Twenty-ninth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1998). Congr. Numer. 133 (1998), 5. 05B15. Listed MR 1 676 510.

It is not known how complete this bibliography is. Additions and corrections are most welcome. Please send them to Fred Rickey, Department of Mathematical Sciences, United States Military Academy, West Point, NY 10996-1786 USA.

Prepared August 2002. Updated November 2005.