Open Research Index

Arthur742Ramos/GraphCoveringTheory

Arthur Freitas Ramos, David Barros Hulak, Ruy J. G. B. de Queiroz

Palomar Registrypalomar/PALOMAR-2026-08-31-000002Aug 31, 2026math.GRscore 0

Formalizes the sharp Schreier index formula for a finite-index subgroup of a free group on a finite nonempty generating type. For a finite nonempty type alpha, a subgroup H of FreeGroup alpha with finite index d is proved equivalent, as a group, to FreeGroup (Fin (1 + d * (card alpha - 1))). More strongly, the repository exposes a FreeGroupBasis for H with this indexing type. The proof realizes H as the vertex group of the finite action-groupoid covering on the coset space, verifies the covering locally by explicit star and costar bijections, and counts the complement of a geodesic spanning…

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