Odd-balanced unimodal sequences and related functions: parity, mock modularity and quantum modularity

Kim, Byungchan; Lim, Subong; Lovejoy, Jeremy

doi:10.1090/proc/13027

Odd-balanced unimodal sequences and related functions: parity, mock modularity and quantum modularity
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by Byungchan Kim, Subong Lim and Jeremy Lovejoy PDF

Proc. Amer. Math. Soc. 144 (2016), 3687-3700 Request permission

Abstract:

We define odd-balanced unimodal sequences and show that their generating function $\mathcal {V}(x,q)$ has the same remarkable features as the generating function for strongly unimodal sequences $U(x,q)$. In particular, we discuss (mixed) mock modularity, quantum modularity, and congruences modulo $2$ and $4$. We also study two related functions which share some of the properties of $U(x,q)$ and $\mathcal {V}(x,q)$.

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