Speaker
Shinya Kawabuchi
(Kumamoto University)
Description
A Steiner system is characterized with the subsets (called blocks) satisfying that all $t$-subsets are included in exactly one block. A perfect matroid design (PMD) is a matroid whose flats of the same rank have the same size. Recently, E. Byrne et. al. proposed a $q$-analogue of PMDs (namely $q$-PMDs) and constructed a non-trivial $q$-PMD from a $q$-analogue of a Steiner system. In this talk, we show some properties of $q$-PMDs and demonstrate that a certain class of $q$-PMDs induces a $q$-Steiner system.
Primary author
Shinya Kawabuchi
(Kumamoto University)
Co-author
Prof.
Keisuke Shiromoto
(Kumamoto University)
