Abstract: Pansymmetry is the abstract of symmetry, stability and other concepts in physics and so on. Fixed pansystems theorems portray a typical pansymmetry of systemic structure. The present paper complements and extends the work in [1]-[3] concerned in fixed pansystems theorems. It gives in finite case the structural character of fixed subsets; the criterion of existence of the least fixed subset, and the numbering formula of fixed subsets and minimal fixed subsets.

Key words: generalized Riemann problem, entropy condition, detonation wave, deflagration wave