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Non-existence of sets of type \(\mathbf (0, 1, 2 , {\varvec{n}}_{{\varvec{d}}})_{{\varvec{d}}}\) in PG(\({\varvec{r,q}}\)) with \(\mathbf 3 \le {\varvec{d}}\le {\varvec{r}}-\mathbf 1 \) and \({\varvec{r}}\ge \mathbf 4 \)

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Abstract

This paper deals with sets of type \((0,1,2,n_{d})_{d}\) in PG(r, q), \(1\le d\le r-1\). The non-existence of sets of type \((0,1,2,n_{d})_{d}\), \(3\le d\le r-1\) in PG(r, q) with \(r\ge 4\) is proved.

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  1. Department of Industrial and Information Engineering and Economics, University of L’Aquila, Piazzale Ernesto Pontieri, 1, Monteluco di Roio, 67100, L’Aquila, Italy

    Mauro Zannetti

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  1. Mauro Zannetti
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Correspondence to Mauro Zannetti.

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Zannetti, M. Non-existence of sets of type \(\mathbf (0, 1, 2 , {\varvec{n}}_{{\varvec{d}}})_{{\varvec{d}}}\) in PG(\({\varvec{r,q}}\)) with \(\mathbf 3 \le {\varvec{d}}\le {\varvec{r}}-\mathbf 1 \) and \({\varvec{r}}\ge \mathbf 4 \). J. Geom. 109, 14 (2018). https://doi.org/10.1007/s00022-018-0419-1

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  • DOI: https://doi.org/10.1007/s00022-018-0419-1

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