Some congruences for 3-component multipartitions

• Autorzy: Tao Yan Zhao , Lily J. Jin , C. Gu
• Języki publikacji: EN

Abstrakty

EN

Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310).

Słowa kluczowe

EN

Congruences; Multipartitions; Theta functions

Kategorie tematyczne

• 11P83: Partitions; congruences and congruential restrictions
• 05A17: Partitions of integers

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 783-788

Daty

wydano

2016-01-01

otrzymano

2016-04-12

zaakceptowano

2016-08-22

online

2016-10-16

Twórcy

autor

Tao Yan Zhao

• Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013,

autor

Lily J. Jin

• School of Mathematics, Nanjing Normal University, Taizhou College, Jiangsu, Taizhou 225300,

autor

C. Gu

• Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013,

Identyfikatory

DOI

10.1515/math-2016-0067