caa a22 4500 475807448 CHVBK 20180406123751.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1008337524556 doi (NATIONALLICENCE)springer-10.1023/A:1008337524556 Mixed Partitions of Projective Geometries [Elektronische Daten] [Arrigo Bonisoli, Antonio Cossidente] Starting from a linear collineation of PG(2n−1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n−1,q) consisting of two (n−1)-subspaces and caps, all having size (qn−1)/(q−1) or (qn−1)/(q+1) according as n is odd or even respectively. Similar partitions of quadrics or hermitian varieties into two maximal totally isotropic subspaces and caps of equal size are also obtained. We finally consider the possibility of partitioning the Segre variety $${\mathcal{S}_{2,2} }$$ of PG(8,q) into caps of size q2+q+1 which are Veronese surfaces. Kluwer Academic Publishers, 2000 cap nationallicence Singer cycle nationallicence mixed partition nationallicence Kronecker product nationallicence Veronese surface nationallicence Bonisoli Arrigo Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100, Potenza, (Italy) aut Cossidente Antonio Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100, Potenza, (Italy) aut Designs, Codes and Cryptography Kluwer Academic Publishers 20/2(2000-06-01), 143-154 0925-1022 20:2<143 2000 20 10623 https://doi.org/10.1023/A:1008337524556 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008337524556 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bonisoli Arrigo Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100, Potenza, (Italy) aut NATIONALLICENCE 700 1- Cossidente Antonio Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100, Potenza, (Italy) aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 20/2(2000-06-01), 143-154 0925-1022 20:2<143 2000 20 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer