Meromorphic differentials generated by an involution identity are proven symmetric in all arguments, via a new combinatorial identity for integer partitions.
Blobbed topological recursion of the quartic Kontsevich model II: Genus=0
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abstract
We prove that the genus-0 sector of the quartic analogue of the Kontsevich model is completely governed by an involution identity which expresses the meromorphic differential $\omega_{0,n}$ at a reflected point $\iota z$ in terms of all $\omega_{0,m}$ with $m\leq n$ at the original point $z$. We prove that the solution of the involution identity obeys blobbed topological recursion, which confirms a previous conjecture about the quartic Kontsevich model.
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Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions
Meromorphic differentials generated by an involution identity are proven symmetric in all arguments, via a new combinatorial identity for integer partitions.