{"id":"palomar/PALOMAR-2026-10-28-000009","url":"https://github.com/jtraverso/stanley/tree/48d36cbaa54d14443f99b57776ce65f1f31c8331","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000009-v1.json","repo":"https://github.com/jtraverso/stanley","tags":["math.CO","msc:05C15","msc:05C20","msc:05C30"],"score":0,"title":"Stanley's acyclic orientations and chromatic reciprocity","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"Acyclic orientations of graphs","identifier":"doi:10.1016/0012-365X(73)90108-8","relationship":"formalizes"}]}