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We study quantum many-body states of immanons, hypothetical particles thatobey an exchange symmetry defined for more than two participating particles.Immanons thereby generalize bosons and fermions, which are defined by theirbehavior under pairwise symmetric and anti-symmetric exchange processes. Thescalar product of two many-body states with fermionic, bosonic or generalizedexchange symmetry becomes the determinant, permanent or immanant of the matrixcontaining all mutual scalar products of the occupied single-particle states.As a measurable consequence, immanons are shown to obey a partial Pauliprinciple that forbids the multiple occupation of single-particle states abovea certain threshold. The tendency to favor or oppose multiple occupation ofsingle-particle modes, i.e. the degree of bunching, is the determinant,permanent or immanant of a hermitian positive semi-definite matrix. We exploitthis identity to devise a Gedankenexperiment that corroborates the permanentaldominance conjecture.

Extending bosons and fermions beyond pairwise exchange symmetry