Harmonic partitions of positive integers and bosonic extension of Euler’s pentagonal number theorem

In this paper, we first propose a cohomological derivation of the celebrated Euler’s Pentagonal Number Theorem. Then we prove an identity that corresponds to a bosonic extension of the theorem. The proof corresponds to a cohomological re-derivation of Euler’s another celebrated identity.

Mathematics Subject Classification. Primary 05A17; Secondary 13D25.