# Alexander Berkovich

## On a new companion to Capparelli partition theorem

#### When/Where:

December 2, 1:55 — 2:45pm at LIT 368.

#### Abstract:

I will report on my recent joint work with Ali Uncu.

In particular, I will prove the following Theorem:

Let $$A(n)$$ be the number of partitions of n of the form $$p_1+ p_2+ p_3 +…$$, where $$p_{2i-r}-p_{2i-r+1} >r$$ for $$r=0$$ or $$1$$. Moreover, $$p_{2i} \not= 2$$ mod $$3$$ and $$p_{2i+1} \not= 1$$ mod $$3$$ .

Let $$C(n)$$ be the number of partitions of $$n$$ into distinct parts $$\not= 1$$ or $$5$$ mod $$6$$.

Then $$A(n) = C(n)$$.

If time permits, I will discuss 3 parameter refinement of this result