
In this paper, we study the minimum co-operative guards problem, a variation of the art gallery problem. First, we show that the minimum number of co-operative guards required for a
In this paper, we construct all symmetric
In this paper, the Desargues Configuration in
Fix a positive integer
modulo
We report on progress towards deciding the existence of
A graph
A problem about “nine foreign journalists” from a Nordic Mathematical Olympiad is used as the starting point for a discussion of a class of extremal problems involving hypergraphs.
Specifically, the problem is to find a sharp lower bound for the maximum degree of the hypergraph in terms of the number of (hyper)edges and their cardinalities.
In [Discrete Math. 111 (1993), 113-123], the
for any
In a group channel, codes correcting and detecting arbitrary patterns of errors (not necessarily “white noise”) are described metrically. This yields sphere-packing and Gilbert bounds on the sizes of all and of maximal codes, respectively. The loop transversal approach builds linear codes correcting arbitrary error patterns. In the binary case, the greedy loop transversal algorithm builds lexicodes.
A
In this paper, we obtain some combinatorial inequalities involving the parameters of a balanced array (B-array)
We call a partition
Let
Furthermore, if
This paper addresses the following questions. In any graph
From any projective plane
it is shown that the binary code of the Hadamard
The \emph{geodetic cover} of a graph
any vertex not in
We exhibit a self-conjugate self-orthogonal diagonal Latin square of order
We consider the problem of scheduling
on a single processor with generalized due dates. The due dates
are given according to positions at which jobs are completed,
rather than specified by the jobs.
We show that the following problems are NP-Complete,
With the removal of precedence constraints, we prove that
the two problems,
are polynomially solvable.
The paper studies linear block codes and syndrome functions built by the greedy loop transversal algorithm. The syndrome functions in the binary white-noise case are generalizations of the logarithm, exhibiting curious fractal properties. The codes in the binary white-noise case coincide with lexicodes; their dimensions are listed for channel lengths up to sixty, and up to three hundred for double errors. In the ternary double-error case, record-breaking codes of lengths
Suppose that a finite group
an injective
holds if the stabilizer of a point in
A Latin square
Let
and one hole of size
A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say
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