Partitions with Congruence Conditions

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Authors

  • S. V. University, Tirupati, A.P. ,IN

Abstract

Let m be a given natural number and a={a1, a2,..., ar}, 1 < a3<m/2, aj≠at,j≠t and let pa(n) denote the number of partitions of the natural number n into summands congruent to ± aj(mod m), aj∈a. In the present paper convergent series and asymptotic formulae are obtained for pa{n). Also for qa(n), the corresponding partition function with distinct summands, the corresponding results are obtained by the author-they are mentioned here omitting details.

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Published

1972-12-01

How to Cite

Subrahmanyasastri, V. V. (1972). Partitions with Congruence Conditions. The Journal of the Indian Mathematical Society, 36(3-4), 177–194. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/16663

 

References

E. GEOSSWALD: Some theorems concerning partitions, Trans. Amer. Math. Soc, Vol. 89 (1958), 113-128.

P. HAOIS, JB . A problem on partition with a prime modulus p > 3, Traits. Amer. Math. Soc, Vol. 102 (1962), 30-62.

P. HAGIS, JR. A class of partitions with distinct summands, Trans. Amer. Math. Soc, Vol. 112 (1964), 401-415.

L. K. HUA: On the number of partitions of a number into unequal parts, Trans. Amer. Math. Soc, Vol. 51 (1942), 194-201.

G. H. HAEDY and S. RAMANUJAN: Asymptotic formulae in combinatory analysis, Proc London Math. Soc, 2nd series, Vol. 17 (1918), 75-115.

S. ISEKI: A partition function with some congruence conditions, Amer. J. Math., Vol. 81 (1959), 939-961.

S. ISEKI: Partitions in certain arithmetic progressions, Amer. J. Math., Vol. 83 (1961), 243-264.

J. LEHNEB: A partition function connected with modulus five, Duke Math. J., Vol. 8 (1941), 631-655.

H. PETEBSSON: t)ber Partitionen probleme in Verbindung mit potenzresten nach einem Primzahlmodul, Math. Zeit., Vol. 66 (1956), 241-68.

H. PETEBSSOK: t)ber Modulfunktionen und Partitionenprobleme, Abhandlungen Deutsche Akademie Wissenchaften Berlin, Kl Math. Allg. Nat. (1954), No. 2.

H. PETEBSSON: Uber arithmetischen Eigen^chaften eines systems multiplikativer Modulfunktionen von Primzahlstufe, Acta Mathematika, Vol. 95 (1956), 57-110.

H. RADEMAOHEB: On the partition function p(n), Proc. London Math. Soc, 2nd series, Vol. 43 (1937), 242-254.

H. RADEMAOHEB: The Fourier coefficients of modular invariant J(T), Amer. J. Math., Vol. 60 (1938), 501-512.