Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Ollis, M. A."'
Autor:
Agirseven, Onur, Ollis, M. A.
Label the vertices of the complete graph $K_v$ with the integers $\{0, 1, \ldots, v-1\}$ and define the {\em length} $\ell$ of the edge between distinct vertices labeled $x$ and $y$ by $\ell(x,y) = \min( |y-x|, v - |y-x| )$. A {\em realization} of a
Externí odkaz:
http://arxiv.org/abs/2402.08736
Autor:
Curran, Stephen J., Ollis, M. A.
A prime labeling on a graph of order $m$ is an assignment of $\{ 1, 2, \ldots, m \}$ to the vertices of the graph such that each pair of adjacent vertices has coprime labels. The ladder of order $2n$ is the $2 \times n$ grid graph graph $P_2 \times P
Externí odkaz:
http://arxiv.org/abs/2306.04088
The partial sums of a sequence ${\mathbf x} = x_1, x_2, \ldots, x_k$ of distinct non-identity elements of a group $(G,\cdot)$ are $s_0 = id_G$ and $s_j = \prod_{i=1}^j x_i$ for $0 < j \leq k$. If the partial sums are all different then ${\mathbf x}$
Externí odkaz:
http://arxiv.org/abs/2301.09367
A subset of an abelian group is {\em sequenceable} if there is an ordering $(x_1, \ldots, x_k)$ of its elements such that the partial sums $(y_0, y_1, \ldots, y_k)$, given by $y_0 = 0$ and $y_i = \sum_{j=1}^i x_i$ for $1 \leq i \leq k$, are distinct,
Externí odkaz:
http://arxiv.org/abs/2203.16658
Autor:
Chand, Pranit, Ollis, M. A.
The Buratti-Horak-Rosa Conjecture concerns the possible multisets of edge-labels of a Hamiltonian path in the complete graph with vertex labels $0, 1, \ldots, {v-1}$ under a particular induced edge-labeling. The conjecture has been shown to hold when
Externí odkaz:
http://arxiv.org/abs/2202.07733
Label the vertices of the complete graph $K_v$ with the integers $\{ 0, 1, \ldots, v-1 \}$ and define the length of the edge between $x$ and $y$ to be $\min( |x-y| , v - |x-y| )$. Let $L$ be a multiset of size $v-1$ with underlying set contained in $
Externí odkaz:
http://arxiv.org/abs/2105.00980
The conjecture, still widely open, posed by Marco Buratti, Peter Horak and Alex Rosa states that a list $L$ of $v-1$ positive integers not exceeding $\left\lfloor \frac{v}{2}\right\rfloor$ is the list of edge-lengths of a suitable Hamiltonian path of
Externí odkaz:
http://arxiv.org/abs/1912.07377
Autor:
Ollis, M. A.
Latin squares with a balance property among adjacent pairs of symbols---being "Roman" or "row-complete"---have long been used as uniform crossover designs with the number of treatments, periods and subjects all equal. This has been generalized in two
Externí odkaz:
http://arxiv.org/abs/1911.12403
Autor:
Ollis, M. A.
Given a subset $S$ of the non-identity elements of the dihedral group of order $2m$, is it possible to order the elements of $S$ so that the partial products are distinct? This is equivalent to the sequenceability of the group when $|S| = 2m-1$ and s
Externí odkaz:
http://arxiv.org/abs/1904.07646
Autor:
Ollis, M. A., Tripp, Christopher R.
We construct sequencings for many groups that are a semi-direct product of an odd-order abelian group and a cyclic group of odd prime order. It follows from these constructions that there is a group-based complete Latin square of order $n$ if and onl
Externí odkaz:
http://arxiv.org/abs/1812.05526