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pro vyhledávání: '"Stinson, A R"'
In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.
Externí odkaz:
http://arxiv.org/abs/2409.08094
One method of constructing $(a^2+1, 2,a, 1)$-SEDFs (i.e., strong external difference families) in $\mathbb{Z}_{a^2+1}$ makes use of $\alpha$-valuations of complete bipartite graphs $K_{a,a}$. We explore this approach and we provide a classification t
Externí odkaz:
http://arxiv.org/abs/2406.09075
Autor:
Stinson, Douglas R.
We study two types of nestings of balanced incomplete block designs (BIBDs). In both types of nesting, we wish to add a point (the nested point) to every block of a $(v,k,\lambda)$-BIBD in such a way that we end up with a partial $(w,k+1,\lambda+1)$-
Externí odkaz:
http://arxiv.org/abs/2405.12820
In a nesting of a balanced incomplete block design (or BIBD), we wish to add a point (the \emph{nested point}) to every block of a $(v,k,\lambda)$-BIBD in such a way that we end up with a partial $(v,k+1,\lambda+1)$-BIBD. In the case where the partia
Externí odkaz:
http://arxiv.org/abs/2404.02666
Autor:
Stinson, Douglas R.
The obvious way to construct a GDD (group-divisible design) recursively is to use Wilson's Fundamental Construction for GDDs (WFC). Then a PBD (pairwise balanced design) is often obtained by adding a new point to each group of the GDD. However, after
Externí odkaz:
http://arxiv.org/abs/2403.17602
(Strong) circular external difference families (which we denote as CEDFs and SCEDFs) can be used to construct nonmalleable threshold schemes. They are a variation of (strong) external difference families, which have been extensively studied in recent
Externí odkaz:
http://arxiv.org/abs/2310.02810
In situations where every item in a data set must be compared with every other item in the set, it may be desirable to store the data across a number of machines in such a way that any two data items are stored together on at least one machine. One w
Externí odkaz:
http://arxiv.org/abs/2309.00213
Autor:
Veitch, Shannon, Stinson, Douglas R.
Various notions of non-malleable secret sharing schemes have been considered. In this paper, we review the existing work on non-malleable secret sharing and suggest a novel game-based definition. We provide a new construction of an unconditionally se
Externí odkaz:
http://arxiv.org/abs/2305.09405
A $k$-dispersed labelling of a graph $G$ on $n$ vertices is a labelling of the vertices of $G$ by the integers $1, \dots , n$ such that $d(i,i+1) \geq k$ for $1 \leq i \leq n-1$. $DL(G)$ denotes the maximum value of $k$ such that $G$ has a $k$-disper
Externí odkaz:
http://arxiv.org/abs/2301.11713
Autor:
Stinson, Douglas R.
In this paper, we study skew frame starters, which are strong frame starters that satisfy an additional "skew" property. We prove three new non-existence results for cyclic skew frame starters of certain types. We also construct several small example
Externí odkaz:
http://arxiv.org/abs/2211.12367