## 1.5Selected Mathematical Concepts and Tools for an Analysis of Infeasible Systems of Constraints

In this section we survey several mathematical concepts and tools discussed in Chapters 2-6, which can be useful in an analysis of infeasible systems of constraints.

Recall that an infeasible monotone system is defined to be a finite nonempty collection ${\mathbb{S}}^{r(M)-1}$ of constraints, together with a map π : (m) 2Γ from the Boolean lattice B(m) of subsets of the index set [m] to the power set of a nonempty set Γ (that is, to the unordered family of all subsets of Γ) such that

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