caa a22 4500 47704073X CHVBK 20180405111317.0 cr unu---uuuuu 170330e19960501xx s 000 0 eng 10.1007/BF00130581 doi (NATIONALLICENCE)springer-10.1007/BF00130581 m -Systems and partial m -systems of polar spaces [Elektronische Daten] [E. Shult, J. Thas] LetP be a finite classical polar space of rankr, withr ≥ 2. A partialm-systemM ofP, with 0 ≤m ≤r - 1, is any set (π1), π2,..., πk ofk (≠ 0) totally singularm-spaces ofP such that no maximal totally singular space containing πi has a point in common with (π1 ∪ π2 ∪... ∪ πk) — πi,i = 1, 2,...,k. In a previous paper an upper bound δ for ¦M¦ was obtained (Theorem 1). If ¦M¦ = δ, thenM is called anm-system ofP. Form = 0 them-systems are the ovoids ofP; form =r - 1 them-systems are the spreads ofP. In this paper we improve in many cases the upper bound for the number of elements of a partialm-system, thus proving the nonexistence of several classes ofm-systems. Kluwer Academic Publishers, 1996 m -system nationallicence partial m -system nationallicence polar space nationallicence Shult E. Department of Mathematics, Kansas State University, Cardwell Hall, 66506-2602, Manhattan, Kansas, USA aut Thas J. Department of Pure Mathematics and Computer Algebra, University of Ghent, Krijgslaan 281, B-9000, Gent, Belgium aut Designs, Codes and Cryptography Kluwer Academic Publishers 8/1-2(1996-05-01), 229-238 0925-1022 8:1-2<229 1996 8 10623 https://doi.org/10.1007/BF00130581 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00130581 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shult E. Department of Mathematics, Kansas State University, Cardwell Hall, 66506-2602, Manhattan, Kansas, USA aut NATIONALLICENCE 700 1- Thas J. Department of Pure Mathematics and Computer Algebra, University of Ghent, Krijgslaan 281, B-9000, Gent, Belgium aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 8/1-2(1996-05-01), 229-238 0925-1022 8:1-2<229 1996 8 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 477040373 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer