Some new congruences for simultaneously s-regular and t-distinct partition function
https://doi.org/10.26907/0021-3446-2024-10-18-21
Abstract
A partition of a positive integer n is said to be simultaneously s-regular and t-distinct partition if none of the parts is divisible by s and parts appear fewer than t times. In this paper, we present some new congruences for simultaneously s-regular and t-distinct partition function denoted by M d (n) with (s, t) (2, 5), (3, 4), (4, 9), (5\alpha, 5\beta ), (7\alpha, 7\beta ), (p, p), where\alpha and \beta are any positive integers and p is any prime.
About the Authors
P. Buragohain
Rajiv Gandhi University
India
India
Pujashree Buragohain
Rono Hills, Doimukh, Arunachal Pradesh, 791112
N. Saikia
Rajiv Gandhi University
India
India
Nipen Saikia
Rono Hills, Doimukh, Arunachal Pradesh, 791112
References
1. Keith W.J. A bijection for partitions simultaneously s-regular and t-distinct, Integers 23 (#A9) (2023).
2. R{e}dseth {O}. Dissections of the generating functions of q(n) and q0(n), Arbok Univ. Bergen Mat. Nat. (12), 3–12 (1970) (MR0434959 (55:7922)).
3. Keith W.J. Partitions into Parts Simultaneously Regular, Distinct, And/or Flat, Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016. Springer Proc. Math. & Statistics, 220.
4. Hirschhorn M.D., Sellers J.A. Elementary proofs of parity results for 5-regular partitions, Bull. Aust. Math. Soc. 81 (1), 58–63 (2010).
5. Hirschhorn M.D. The Power of q, A Personal Journey, Vol. 49, Developments in Mathematics (Springer, Cham, 2017).
6. Berndt B.C. Ramanujan’s Notebooks, Part III (Springer-Verlag, New York, 1991).
7. Cui S.P., Gu N.S.S. Arithmetic properties of ell -regular partitions, Adv. Appl. Math. 51, 507–523 (2013).
Review
For citations:
Buragohain P., Saikia N. Some new congruences for simultaneously s-regular and t-distinct partition function. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(10):18-21. (In Russ.) https://doi.org/10.26907/0021-3446-2024-10-18-21
Views:
146
Email this article 