SOME CONGRUENCES FOR (S, T )-REGULAR BIPARTITIONS MODULO T

摘要

In this work, we study the function Bs,t(n), which counts the number of (s, t)- regular bipartitions of n. Recently, many authors proved the existence of infinite families of congruences modulo 11 for B3,11(n), modulo 3 for B3,s(n) and modulo 5 for B5,s(n). Most recently, the first author proved the existence of infinite families of congruences modulo 11, 13 and 17 for B5,11(n), B5,13(n) and B81,17(n), respectively. In this paper, we establish the existence of infinite families of congruences modulo 5 for B2,15(n), modulo 11 for B7,11(n), modulo 11 for B27,11(n) and modulo 17 for B243,17(n).