Congruences modulo 9 for bipartitions with  designated summands

Robert Xiaojian HAO; ERIN YIYING SHEN

Article Details

Congruences modulo 9 for bipartitions with designated summands

Authors:

Robert Xiaojian HAO | ERIN YIYING SHEN

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2325-2335

Document Type:

Article

Publication Date:

9/2018

Document Language:

Turkish

Document ID (Org No.):

2000745764

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

Andrews, Lewis, and Lovejoy studied arithmetic properties of partitions with designated summands that are defined on ordinary partitions by tagging exactly one part among parts with equal size. A bipartition of nnn is an ordered pair of partitions (π1,π2)(π1,π2)(\pi_1, \pi_2) with the sum of all of the parts being nnn. In this paper, we investigate arithmetic  properties of  bipartitions with designated summands.  Let PD−2(n)PD−2(n)PD_{-2}(n) denote the number of bipartitions of nnn with designated summands. We establish several Ramanujan-like congruences and  an infinite family of congruences modulo 999 satisfied by  PD−2(n)PD−2(n)PD_{-2}(n).

Article Details

Congruences modulo 9 for bipartitions with designated summands

Authors: Robert Xiaojian HAO | ERIN YIYING SHEN

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2325-2335

Document Type: Article

Publication Date: 9/2018

Document Language: Turkish

Document ID (Org No.): 2000745764

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Robert Xiaojian HAO | ERIN YIYING SHEN

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2325-2335

Document Type:

Article

Publication Date:

9/2018

Document Language:

Turkish

Document ID (Org No.):

2000745764

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098