This white paper explores the rigorous structure of enumerative combinatorics through functions, functors, and minimal computational frameworks (Lisp and lambda calculus).

We define combinations and permutations formally, investigate general counterexamples, and propose extensions to homotopy, category theory, and quantum-inspired thought experiments.

Emphasis is placed on connecting classical combinatorial principles to topological and categorical structures, providing formal proofs, propositions, and functional algorithms suitable for both theoretical and practical applications.

Design

Abstract

This white paper explores the rigorous structure of enumerative combinatorics through functions, functors, and minimal computational frameworks (Lisp and lambda calculus). 

We define combinations and permutations formally, investigate general counterexamples, and propose extensions to homotopy, category theory, and quantum-inspired thought experiments. 

Emphasis is placed on connecting classical combinatorial principles to topological and categorical structures, providing formal proofs, propositions, and functional algorithms suitable for both theoretical and practical applications.