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