We obtain a condition describing when the quasimodular forms given by the
Bloch-Okounkov theorem as $q$-brackets of certain functions on partitions are
actually modular. This condition involves the kernel of an operator {\Delta}.
We describe an explicit basis for this kernel, which is very similar to the
space of classical harmonic polynomials.Comment: 12 pages; corrected typo

van Ittersum, Jan-Willem M.

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arXiv

We obtain a condition describing when the quasimodular forms given by the Bloch–Okounkov theorem as q-brackets of certain functions on partitions are actually modular. This condition involves the kernel of an operator Δ. We describe an explicit basis for this kernel, which is very similar to the space of classical harmonic polynomials

When is the Bloch-Okounkov q-bracket modular?

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