What is in #P and what is not?

Christian Ikenmeyer; Igor Pak

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arXiv · 2204.13149

What is in #P and what is not?

Christian Ikenmeyer·Igor Pak

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Abstract

For several classical nonnegative integer functions, we investigate if they are members of the counting complexity class #P or not. We prove #P membership in surprising cases, and in other cases we prove non-membership, relying on standard complexity assumptions or on oracle separations. We initiate the study of the polynomial closure properties of #P on affine varieties, i.e., if all problem instances satisfy algebraic constraints. This is directly linked to classical combinatorial proofs of algebraic identities and inequalities. We investigate #TFNP and obtain oracle separations that prove the strict inclusion of #P in all standard syntactic subclasses of #TFNP-1.

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Christian Ikenmeyer, Igor Pak. 2022-04-27. What is in #P and what is not?. https://arxiv.org/abs/2204.13149

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