Open Research Index

Stanley's acyclic orientations and chromatic reciprocity

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-28-000009Oct 28, 2026math.COscore 0

For every finite simple graph and k ≥ 0, the signed evaluation (−1)^n χ_G(−k) counts acyclic orientations paired with weakly compatible Fin k colorings (Stanley 1973, Theorem 1.2); at k = 1 it counts acyclic orientations (Corollary 1.3). Includes positive-evaluation correctness, induced-subgraph convolution, and the finite equivalence between well-foundedness and no directed cycles.

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