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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 $h_m (n)$.
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참고문헌 (17)
참고문헌 신청
G. E. Andrews / 1971 / Congruence properties of the m-ary partition function / J. Number Theory 3:104~110
B. P. Bates / 2006 / Linkages between the Gauss map and the Stern-Brocot tree / Acta Math. Acad. Paedagog. Nyh´az 22(3):217~235
B. P. Bates / 2010 / Locating terms in the Stern-Brocot tree / European J. Combin 31(3):1020~1033
B. P. Bates / 2010 / Linking the Calkin-Wilf and Stern-Brocot trees / European J. Combin 31(7):1637~1661
B. Bates / 2011 / The q-Calkin-Wilf tree / J. Combin. Theory Ser. A 118(3):1143~1151
B. P. Bates / 2006 / Linkages between the Gauss map and the Stern-Brocot tree / Acta Math. Acad. Paedagog. Nyh´az 22(3):217~235
B. P. Bates / 2010 / Locating terms in the Stern-Brocot tree / European J. Combin 31(3):1020~1033
B. P. Bates / 2010 / Linking the Calkin-Wilf and Stern-Brocot trees / European J. Combin 31(7):1637~1661
B. Bates / 2011 / The q-Calkin-Wilf tree / J. Combin. Theory Ser. A 118(3):1143~1151
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