  We introduce a generalization of immanants of matrices, using partition
algebra characters in place of symmetric group characters. We prove that our
immanant-like function on square matrices, which we refer to as the
recombinant, agrees with the usual definition for immanants for the special
case whereby the vacillating tableaux associated with the irreducible
characters correspond, according to the Bratteli diagram for partition algebra
representations, to the integer partition shapes for symmetric group
characters. In contrast to previously studied variants and generalizations of
immanants, as in Temperley-Lieb immanants and $f$-immanants, the sum that we
use to define recombinants is indexed by a full set of partition diagrams, as
opposed to permutations.
