Congruence Properties Of Regular Bipartition Functions

This thesis studies systematically the congruence properties of regular bipartition functions,and establishes several families of congruences modulo 5 for regular bipartition functions.The specific work is as follows:In Chapter 1,we introduce the research background and significance of partition and its congruence,explain briefly the basic concepts,properties and research status of regular bipartition.In Chapter 2,we recall several methods to prove the congruence of regular bipartition functions.For example,the cubic theta function,Euler's pentagonal number theorem and Jacobi's identity are used to prove the congruence.In Chapter 3,we establish three families of congruences modulo 5 for regular bipartition based on the proof method which introduced in the previous chapter.In Chapter 4,we summarize the thesis.