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The distinguishing result of this paper is a $\mathbf{P}$-time enumerablepartition of all the potential perfect matchings in a bipartite graph. Thispartition is a set of equivalence classes induced by the missing edges in thepotential perfect matchings.  We capture the behavior of these missing edges in a polynomially boundedrepresentation of the exponentially many perfect matchings by a graph theoreticstructure, called MinSet Sequence, where MinSet is a P-time enumerablestructure derived from a graph theoretic counterpart of a generating set of thesymmetric group. This leads to a polynomially bounded generating set of all theclasses, enabling the enumeration of perfect matchings in polynomial time. Thesequential time complexity of this $\mathbf{\#P}$-complete problem is shown tobe $O(n^{45}\log n)$.  And thus we prove a result even more surprising than $\mathbf{NP = P}$, thatis, $\mathbf{\#P}=\mathbf{FP}$, where $\mathbf{FP}$ is the class of functions,$f: \{0, 1\}^* \rightarrow \mathbb{N} $, computable in polynomial time on adeterministic model of computation.

An Extension of the Permutation Group Enumeration Technique (Collapse of the Polynomial Hierarchy: $\mathbf{NP = P}$)