Transitive (q-1)-fold packings of \rmPG_n(q)

2024/02/01 by Daniel R. Hawtin, Hawtin, Daniel R.
Engineering · Mathematics · #05B25 (Primary) 05B40 #52C17 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2402.00780

openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A t-fold packing of a projective space \rmPG_n(q) is a collection P of line-spreads such that each line of \rmPG_n(q) occurs in precisely t spreads in P. A t-fold packing P is transitive if a subgroup of \rmPΓL_n+1(q) preserves and acts transitively on P. We give a construction for a transitive (q-1)-fold packing of \rmPG_n(q), where q=2^k, for any odd positive integers n and k, such that n≥ 3. This generalises a construction of Baker from 1976 for the case q=2.

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