Extremal sizes of subspace partitions
2012 (English)In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 64, no 3, 265-274 p.Article in journal (Refereed) Published
A subspace partition I of V = V(n, q) is a collection of subspaces of V such that each 1-dimensional subspace of V is in exactly one subspace of I . The size of I is the number of its subspaces. Let sigma (q) (n, t) denote the minimum size of a subspace partition of V in which the largest subspace has dimension t, and let rho (q) (n, t) denote the maximum size of a subspace partition of V in which the smallest subspace has dimension t. In this article, we determine the values of sigma (q) (n, t) and rho (q) (n, t) for all positive integers n and t. Furthermore, we prove that if n a parts per thousand yen 2t, then the minimum size of a maximal partial t-spread in V(n + t -1, q) is sigma (q) (n, t).
Place, publisher, year, edition, pages
2012. Vol. 64, no 3, 265-274 p.
Subspace partition, Vector space partitions, Partial t-spreads
Mathematics Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-99054DOI: 10.1007/s10623-011-9572-3ISI: 000305520100004ScopusID: 2-s2.0-84863780799OAI: oai:DiVA.org:kth-99054DiVA: diva2:541572
QC 201207192012-07-192012-07-132012-07-19Bibliographically approved