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Three different ways to obtain the values of hyper $m$-ary partition functions

정경아|손재범|Jiae Eom
대한수학회 (The Korean Mathematical Society)|2016.11|대한수학회보 (Bulletin of the KMS)|제53권 제6호|pp. 1857-1868

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참고문헌

키워드

hyper $m$-ary partition functionhyper $m$-ary tree
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초록

We consider a natural generalization of $ h_2 (n) $, denoted \linebreak $ h_m (n) $, which is the number of partitions of $n$ into parts which are power of $m \geq 2$ wherein each power of $m$ is allowed to be used as a part at most $m$ times. In this note, we approach in three different ways using the recurrences, the matrix and the tree to calculate the value of $h_m (n)$.

Abstract

We consider a natural generalization of $ h_2 (n) $, denoted \linebreak $ h_m (n) $, which is the number of partitions of $n$ into parts which are power of $m \geq 2$ wherein each power of $m$ is allowed to be used as a part at most $m$ times. In this note, we approach in three different ways using the recurrences, the matrix and the tree to calculate the value of $h_m (n)$.

참고문헌 (17)

  1. G. E. Andrews, "Congruence properties of the m-ary partition function", J. Number Theory, 3, pp.104~110 (1971)
  2. B. P. Bates, "Linkages between the Gauss map and the Stern-Brocot tree", Acta Math. Acad. Paedagog. Nyh´az, 22(3), pp.217~235 (2006)
  3. B. P. Bates, "Locating terms in the Stern-Brocot tree", European J. Combin, 31(3), pp.1020~1033 (2010)
  4. B. P. Bates, "Linking the Calkin-Wilf and Stern-Brocot trees", European J. Combin, 31(7), pp.1637~1661 (2010)
  5. B. Bates, "The q-Calkin-Wilf tree", J. Combin. Theory Ser. A, 118(3), pp.1143~1151 (2011)
  6. N. Calkin, "Recounting the rationals", Amer. Math. Monthly, 107(4), pp.360~363 (2000)
  7. R. Churchhouse, "Congruence properties of the binary partition function", Proc. Cambridge Philos. Soc, 66, pp.371~376 (1969)
  8. K. M. Courtright, "Arithmetic properties for hyper m-ary partition functions", Integers, 4(A6), pp.5~ (2004)
  9. G. Dirdal, "On restricted m-ary partitions", Math. Scand, 37(1), pp.51~60 (1975)
  10. G. Dirdal, "Congruences for m-ary partitions", Math. Scand, 37(1), pp.76~82 (1975)
  11. L. L. Dolph, "Congruences for a restricted m-ary partition function", Discrete Math, 219, pp.265~269 (2000)
  12. H. Gupta, "On m-ary partitions", Proc. Cambridge Philos. Soc, 71, pp.343~345 (1972)
  13. Q. L. Lu, "On a restricted m-ary partition function", Discrete Math, 275(1-3), pp.347~353 (2004)
  14. B. Reznick, "Analytic number theory", pp.451~477 (1990), Birkhauser
  15. Ø. Rødseth, "Some arithmetical properties of m-ary partitions", Proc. Cambridge Philos. Soc, 68, pp.447~453 (1970)
  16. Ø. Rødseth, "On m-ary partition function congruences: a fresh look at a past problem", J. Number Theory, 87(2), pp.270~281 (2001)
  17. Ø. Rødseth, "On m-ary overpartitions", Ann. Comb, 9(3), pp.345~353 (2005)

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