A new algorithm for finding the full set of minimal defining sets of t-designs
Sule Yazici (Koc University, Istanbul, Turkey)
MSI Computational Mathematics Seminar SeriesDATE: 2007-08-13
TIME: 11:00:00 - 12:00:00
LOCATION: John Dedman G35
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ABSTRACT:
A $t-(v,k,\lambda_{t})$ design D, for $t\geq 0$, is an ordered pair $(V,B)$, where $V$ is a set of $v$ elements, called points, $B$ is a collection (multiset) of $k$-subsets of $V$, called blocks, such that each $t$-subset of $V$ belongs to exactly $\lambda_{t}$ blocks. A defining set of a $t-(v,k,\lambda_{t}$) design is a set of blocks which is a subset of a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper subsets is a defining set. A smallest defining set is one with smallest cardinality. This talk will summaries the ideas of earlier algorithms and proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given $t$-design. The complete list of minimal defining sets of the full $2-(7,3,5)$ design, $2-(15,3,1)$ designs, $2-(25,5,1)$ design and $2-(31,6,1)$ design were found. Some new theoretical technics will also be given for finding the minimal defining sets of $t-(v,k,\lambda_{t})$ designs.
BIO:
http://home.ku.edu.tr/~eyazici/
