Oxenham, Martin and Casse, Rey:
Towards the determination of the regular $n$-covers of $PG(3,q)$
Bollettino dell'Unione Matematica Italiana Serie 8 6-B (2003), fasc. n.1, p. 57-87, Unione Matematica Italiana (English)
pdf (350 Kb), djvu (373 Kb). | MR1955697 | Zbl 1177.51007
Sunto
Si dice che un insieme $S$ di rette di $PG(3, q)$ copre $n$ volte un punto $P$ di $PG(3, q)$, se esistono esattamente $n$ rette di $S$ incidenti $P$. Un insieme di rette di $PG(3, q)$ che copre $n$ volte ogni punto di $PG(3, q)$ si dice $n$-cover. In questa nota, dopo una descrizione degli esempi noti di $n$-cover e delle rispettive proprietà, viene mostrato come gli $n$-cover di $PG(3, q)$ possono essere utilizzati per la costruzione di classi di disegni di Sperner quasi-$n$-multipli. Infine, allo scopo di ottenere nuovi esempi di tali disegni mediante la derivazione di quelli esistenti, si introduce la nozione di n-cover regolare. I risultati principali sono: la dimostrazione della non esistenza di un $2$-cover regolare di $PG(3, q)$ per $q>2$ e quella della non esistenza di un $n$-cover regolare $(n\geq 3)$ per $q\geq n+2$.
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