Some congruences for 3-component multipartitions

Tao Yan Zhao; Lily J. Jin; C. Gu

Open Mathematics (2016)

  • Volume: 14, Issue: 1, page 783-788
  • ISSN: 2391-5455

Abstract

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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).

How to cite

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Tao Yan Zhao, Lily J. Jin, and C. Gu. "Some congruences for 3-component multipartitions." Open Mathematics 14.1 (2016): 783-788. <http://eudml.org/doc/287119>.

@article{TaoYanZhao2016,
abstract = {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).},
author = {Tao Yan Zhao, Lily J. Jin, C. Gu},
journal = {Open Mathematics},
keywords = {Congruences; Multipartitions; Theta functions; multipartitions; congruences; theta functions},
language = {eng},
number = {1},
pages = {783-788},
title = {Some congruences for 3-component multipartitions},
url = {http://eudml.org/doc/287119},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Tao Yan Zhao
AU - Lily J. Jin
AU - C. Gu
TI - Some congruences for 3-component multipartitions
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 783
EP - 788
AB - 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).
LA - eng
KW - Congruences; Multipartitions; Theta functions; multipartitions; congruences; theta functions
UR - http://eudml.org/doc/287119
ER -

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