20200715 季青 Overpartitions and Bressoud’s conjecture

In this talk, we introduce a new partition function $\overline{B}_j$ which could be viewed as an overpartition analogue of the partition function $B_j$ introduced by Bressoud. By constructing bijections, we showed that there is a relationship between $\overline{B}_1$ and ${B}_0$ and a relationship between $\overline{B}_0$ and ${B}_1$. Based on these two relations, we could obtain overpartition analogues of many classical partition theorem including Euler's partition theorem.  In particular, we prove Bressoud's conjecture for j = 0 by establishing an overpartition analogue of Bressoud’s conjecture for $j =1$.  The generating function of the overpartition analogue of Bressoud’s conjecture  is also obtained with the aid of Bailey pairs.
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