Ayrışımların Modulo 11 Kongrüans Özellikleri
Atkin and Swinnerton – Dyer calculated some congruences properties of the generating function for the partitions for modulo 5, 7 and 11. They obtained the results directly for modulo 5 and 7, but for modulo 11, they gave the congruences, and proved later by using these congruences. In this paper, it is explained how the congruences given by Atkin and Swinnerton – Dyer can be calculated for modulo 11.
Anahtar Kelimeler:
Partitions, Partition Function, Partition Congruences.
Congruences Properties of Partitions for Modulo
Atkin and Swinnerton – Dyer calculated some congruences properties of the generating function for the partitions for modulo 5, 7 and 11. They obtained the results directly for modulo 5 and 7, but for modulo 11, they gave the congruences, and proved later by using these congruences. In this paper, it is explained how the congruences given by Atkin and Swinnerton – Dyer can be calculated for modulo 11.
Keywords:
Partitions, Partition Function, Partition Congruences.,
___
- Andrews, G.E. & Garvan F.G. (1988). Dyson’s Crank of a Partition. Bulletin of the American Mathematical Society, 167 – 171.
- Atkin, A.O.L. & Swinnerton – Dyer, H.P.F. (1954). Some Properties of Partitions. Proceedings of the London Mathematical Society, 4, 84 – 106.
- Dyson, F.J. (1944). Some Guesses in Theory of Partitions. Eureka, Cambridge, 8, 10 – 15,.
- Garvan, F.G. (1988). New Combinatorial Interpretations of Ramanujan's Partition Congruences mod 5,7 and 11. Trans. Amer. Math. Soc., 305, 47—77.
- Hardy, G. H., Ramanujan, S. (1918). Asymptotic Formulae in Combinatory Analysis. Proc. London Math. Soc., 17, 75-115.
- Hirschhorn, M.D. (1987). A Generalization of Winquist’s Identity and a Conjecture of Ramanujan. Journal of Indian Mathematical Society, 51.
- Hirschorn, M. D. (1999). Another Short Proof of Ramanujan's Mod 5 Partition Congruences and More. Amer. Math. Monthly, 106, 580-583.
- Lewis, R. (1995). The Components of Modular Forms. J. London Math.Soc., 52 (2), 245-254.
- MacMahon, P. A. (1926). The Parity of p(n), the Number of Partitions of n., when n 1000. J. London Math. Soc. 1, 225-226.
- Ramanujan, S. (1927). Some Properties of p(n), the Number of partitions of n. Paper 25 of Collected Papers of S. Ramanujan, Cambridge University Pres, London.
- Skiena, S. (1990). Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley.
- Winquist, L. (1968). An Elementary Proof of p (11m
- (mod 11). J. Combinatorial 6) Theory, 6, 56-69.
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2010
- Yayıncı: Burdur Mehmet Akif Ersoy Üniversitesi
Sayıdaki Diğer Makaleler
Karagöl (Çubuk, Ankara) Mesire Alanının Bryofit (Bryophyta) Florası
Kerem CANLI, Özcan ŞİMŞEK, Serhat URSAVAŞ, Barbaros ÇETİN
Bazı Su Mercimeklerinin Nutrient Gideriminde Kullanımı
Murat TOPAL, Bünyamin KARAGÖZOĞLU, Erdal ÖBEK, E.işıl Arslan TOPAL
Hava Isıtmalı Güneş Kollektörlerin’de Güneş Takip Mekanizması Kullanımı
İbrahim KIRBAŞ, Bilal AYDOĞAN, Ahmet UYUMAZ
Ayrışımların Modulo 11 Kongrüans Özellikleri
Neslihan ERDOĞAN, Osman KETENOĞLU, M. Ümit BİNGÖL, Fatmagül GEVEN, Münevver ARSLAN