Zobrazeno 1 - 10
of 216
pro vyhledávání: '"ÖSTERGÅRD, PATRIC R. J."'
Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier p
Externí odkaz:
http://arxiv.org/abs/2303.01207
Several methods for generating random Steiner triple systems (STSs) have been proposed in the literature, such as Stinson's hill-climbing algorithm and Cameron's algorithm, but these are not yet completely understood. Those algorithms, as well as som
Externí odkaz:
http://arxiv.org/abs/2208.12057
Steiner triple systems form one of the most studied classes of combinatorial designs. Configurations, including subsystems, play a central role in the investigation of Steiner triple systems. With sporadic instances of small systems, ad-hoc algorithm
Externí odkaz:
http://arxiv.org/abs/2110.00320
The chromatic index of a cubic graph is either 3 or 4. Edge-Kempe switching, which can be used to transform edge-colorings, is here considered for 3-edge-colorings of cubic graphs. Computational results for edge-Kempe switching of cubic graphs up to
Externí odkaz:
http://arxiv.org/abs/2105.01363
The smallest open case for classifying Steiner triple systems is order 21. A Steiner triple system of order 21, an STS(21), can have subsystems of orders 7 and 9, and it is known that there are 12,661,527,336 isomorphism classes of STS(21)s with sub-
Externí odkaz:
http://arxiv.org/abs/2104.06825
Autor:
Kokkala, Janne I., Meagher, Karen, Naserasr, Reza, Nurmela, Kari J., Östergård, Patric R. J., Stevens, Brett
A covering array $\rm{CA}(N;t,k,v)$ of strength $t$ is an $N \times k$ array of symbols from an alphabet of size $v$ such that in every $N \times t$ subarray, every $t$-tuple occurs in at least one row. A covering array is \emph{optimal} if it has th
Externí odkaz:
http://arxiv.org/abs/1901.03594
A finite set of distinct vectors $\mathcal{X}$ in the $d$-dimensional Euclidean space $\mathbb{R}^d$ is called an $s$-distance set if the set of mutual distances between distinct elements of $\mathcal{X}$ has cardinality $s$. In this paper we present
Externí odkaz:
http://arxiv.org/abs/1804.06040
In this paper Seidel matrices are studied, and their spectrum and several related algebraic properties are determined for order $n\leq 13$. Based on this Seidel matrices with exactly three distinct eigenvalues of order $n\leq 23$ are classified. One
Externí odkaz:
http://arxiv.org/abs/1703.02943
Autor:
Brandt, Sebastian, Hirvonen, Juho, Korhonen, Janne H., Lempiäinen, Tuomo, Östergård, Patric R. J., Purcell, Christopher, Rybicki, Joel, Suomela, Jukka, Uznański, Przemysław
LCLs or locally checkable labelling problems (e.g. maximal independent set, maximal matching, and vertex colouring) in the LOCAL model of computation are very well-understood in cycles (toroidal 1-dimensional grids): every problem has a complexity of
Externí odkaz:
http://arxiv.org/abs/1702.05456
We determine that there is no partial geometry ${\cal G}$ with parameters $(s,t,\alpha)=(4,27,2)$. The existence of such a geometry has been a challenging open problem of interest to researchers for almost 40 years. The particular interest in ${\cal
Externí odkaz:
http://arxiv.org/abs/1607.03372