Categorification demonstrates a generating function for partial duals in ribbon graphs, suggesting new perspectives in algebraic topology.
The partial-dual genus polynomial ∂εG(z) of a ribbon graph G is the generating function that enumerates all partial duals of G. We exhibit a categorification for this polynomial. The key ingredient of the construction is an extended Frobenius algebra related to unoriented topological quantum field theory.
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Cheng et al. (2026) studied this question.
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