http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
On 5-regular bipartitions with odd parts distinct
M. S. MAHADEVA NAIKA,HARISHKUMAR T. 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.2
In his work, K. Alladi [1] considered the partition function pod(n), the number of partitions of an integer n with odd parts distinct (the even parts are unrestricted). Later Hirschhorn and Sellers [8] obtained some internal congruences involving innite families of Ramanujan-type congruences for pod(n). Let Bo(n) denote the number of 5-regular bipartitions of a positive integer n with odd parts distinct. In this paper, we establish many innite families of congruences modulo powers of 2 for Bo(n). For example, Bo 32 34 52+2 72 n + t7 34 52+1 72 1 0 (mod 16); for ; ; 0 and t7 2 f28; 92; 124; 156g.
On (3,4)-regular bipartitions with designated summands
M. S. MAHADEVA NAIKA,HARISHKUMAR T.,Y. VEERANNA 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.4
Andrews, Lewis and Lovejoy defined a new class of partitions with designated sum-mands by taking ordinary partitions and tagging exactly one of each part size. Let BPD3,4(n) denote the number of bipartitions of n with designated summands in which parts are not multiples of 3 or 4. In this paper, we establish many infinite families of congruences modulo powers of 2 for BPD3,4(n). For example, for any n≥0 and α,β,γ≥0, BPD3,4(24·32α·52β+2·72γn+b1·32α·52β+1·72γ)≡0 (mod 4), where b1∈{39, 63, 87, 111}.