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Andrews, G., Congruence properties of the m-ary partition function, J. Number Theory, 3 (1971), 104–110. MR 42#3043.
Andrews, G., The Theory of Partitions. Encyc. of Math, and Appl., v. 2, Addison-Wesley, Reading 1976, MR 58#27738.
de Bruijn, N. G., On Mahler’s partition problem, Indag. Math. 10 (1948), 210–220. MR 10, 16d.
Carlitz, L., A problem in partitions related to the Stirling numbers, Riv. Mat. Univ. Parma 5 (1964), 61–75. MR 34#158.
Carlitz, L., A problem in partitions related to the Stirling numbers, Bull. Amer. Math. Soc. 70 (1964), 275–278. MR 28#1135.
Carlitz, L., Generating functions and partition problems. Pp. 144–169, in Proc. Sympos. Pure Math. VIII, Amer. Math. Soc., Providence, 1965, MR 31 #72.
Churchhouse, R. F., Congruence properties of the binary partition function, Proc. Camb. Phil. Soc. 66 (1969), 371–376. MR 40#1356.
Dirdal, G., On restricted m-ary partitions, Math. Scand. 37 (1975), 51–60. MR 52#10582.
Dirdal, G., Congruences for m-ary partitions, Math. Scand. 37 (1975), 76–82. MR 52#10583.
Euler, L., Introductio in analysin infinitorum. Lausanne, 1748, in Opera Omnia Series Prima Opera Math. vol. 8, B. G. Teubner, Leipzig, 1922.
Euler, L., De partitione numerorum, Nov. com. acad. sci. Petro. 3 (1750/1751), 125–169. In Opera Omnia Series Prima Opera Math, vol. 2, pp. 254–294, B. G. Teubner, Leipzig, 1915.
Gupta, H., Proof of the Churchhouse conjecture concerning binary partitions, Proc. Camb. Phil. Soc. 70 (1971), 53–56. MR 45#4986.
Gupta, H., A simple proof of the Churchhouse conjecture concerning binary partitions, Ind. J. Pure Appl. Math. 3 (1972), 791–794. MR 48#8377.
Gupta, H., On m-ary partitions, Proc. Camb. Phil. Soc 71 (1972), 343–345. MR 45#204.
Gupta, H., A direct proof of the Churchhouse conjecture concerning binary partitions, Ind. J. Math. 18 (1976), 1–5. MR 82b:10013.
Gupta, H. and P. A. B. Pleasants, Partitions into powers of m, Ind. J. Pure Appl. Math. 10 (1979), 655–694. MR 80f:10014.
Hirschhorn, M. D. and J. H. Loxton, Congruence properties of the binary partition function, Proc. Camb. Phil. Soc. 78 (1975), 437–442. MR 52#3045.
Klosinski, L. F., G. L. Alexanderson and A. P. Hillman, The William Lowell Putnam Mathematical Competition, Amer. Math. Monthly 91 (1984), 487–495.
Knuth, D. E., An almost linear recurrence, Fib. Q. 4 (1966), 117–128. MR 33#7317.
Lehmer, D. H., On Stern’s diatomic series, Amer. Math. Monthly 36 (1929), 59–67.
Lind, D. A., An extension of Stern’s diatomic series, Duke Math. J. 36 (1969), 55–60. MR 30 #6810.
Lucas, É., Sur les suites de Farey, Bull. Soc. Math. France (1877–1878), 118–119.
Mahler, K., On a special functional equation, J. London Math. Soc. 15 (1940), 115–123. MR 2, 133e.
Reznick, B., Digital representations using the greatest integer function, Trans. Amer. Math. Soc. 312 (1989), 355–375. MR 89g:11010.
Reznick, B., Congruence properties of the Stem sequence, in preparation.
Reznick, B., Stern measures, in preparation.
de Rham, G., Un peu de mathématiques à propos d’une courbe plane, Elem. Mat. 2 (1947), 73–76, 89–97. MR 9–246.
Rödseth, 0, Some arithmetical properties of m-ary partitions, Proc. Camb. Phil. Soc. 68 (1970), 447–453. MR 41#5319.
Sloane, N. J. A., A Handbook of Integer Sequences, Academic Press, New York (1973). MR 50#9760.
Stanley, R. P. Private communication.
Stern, M. A., Ueber eine zahlentheoretische funktion, J. fur Math. 55 (1858), 193–220.
Tanturri, A, Della partizione dei numeri. Ambi, terni quaterne e cinquine di data somma, Att. delle Sci. di Torino 52 (1916/7), 902–918.
Tanturri, A, Sul numero delle partizioni d’un numero in potenze di 2, Att. delle Sci. di Torino 54 (1918), 97–110.
Tanturri, A., Sul numero delle partizioni d’un numero in potenze di 2, Att. Accad. Naz. Lincei 27 (1918), 399–403.
Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois, USA
Bruce Reznick
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Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 west Green Street, 61801, Urbana, Illinois, USA
Bruce C. Berndt , Harold G. Diamond , Heini Halberstam & Adolf Hildebrand , , &
Dedicated to Professor T. Bateman on the occasion of his retirement
© 1990 Birkhäuser Boston
Reznick, B. (1990). Some Binary Partition Functions. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_29
DOI: https://doi.org/10.1007/978-1-4612-3464-7_29
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Print ISBN: 978-0-8176-3481-0
Online ISBN: 978-1-4612-3464-7
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