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We introduce the non-commutative subset convolution-a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of quaternions used mainly in the quantum field theory. We apply this tool to speed up algorithms counting subgraphs parameterized by the treewidth of a graph. We present an O ∗ ( ( 2 ω + 1 ) tw ) -time algorithm for counting Steiner trees and an O ∗ ( ( 2 ω + 2 ) tw )doi:10.1007/s00453-018-0489-3 pmid:30872883 pmcid:PMC6386049 fatcat:nv3dazhwrngczjn4bcr5hkxdqu