
Let
A border of a string
In developing an observation made by the author concerning a class of expansions of the sine function, M. Xinrong has recently analysed the question of a generalised form through a succinct use of linear operator theory. This paper constitutes an extension of his work, in which the current problem is solved completely by examining the generating function of a finite sequence central to the formulation.
For graphs
For
is a constant map. We denote the set of all k such that G is k-magic by IM(G). We call this set as the \textbf{integer-magic spectrum} of G. This paper deals with determining the integer-magic spectra of powers of paths
A new graph labeling problem on simple graphs called edge-balanced labeling is introduced by Kong and Lee [11]. They conjectured that all trees except
Let
By definition, the vertices of a de Bruijn graph are all strings of length
Given two graphs
In this paper, we discuss a self-adjusting and self-improving combinatorial optimization algorithm. Variations of this algorithm have been successfully applied in recent research in Design Theory. The approach is simple but general and can be applied in any instance of a combinatorial optimization problem.
Let
Let
Let
A (p,q) graph G is \emph{total edge-magic} if there exists a bijection
For
is a constant map. We denote the set of all
Several
We describe a concrete data structure, called a sequence-tree, that represents sequences of arbitrary elements, along with associated algorithms that allow single element access and assignment, subsequence extraction (slicing), and concatenation to be done in logarithmic time relative to sequence length. These operations are functional, in the sense that they leave their operand sequences unchanged. For a single sequence, space is linear in the sequence length. Where a set of multiple sequences have been computed by these algorithms, space may be sublinear, because of node sharing. Sequence-trees use immutable, shared, dynamically allocated nodes and thus may require garbage collection, if some of the sequences in a set are abandoned. However, the interconnection of nodes is non-cyclic, so explicitly programmed collection using reference counting is reasonable, should a general-purpose garbage collector be unavailable. Other sequence representations admit only to linear-time algorithms for one or more of the aforementioned operations. Thus sequence-trees give improved performance in applications where all the operations are needed.
This paper is an expository treatment of the Leftover Hash Lemma and some of its applications in cryptography and complexity theory.
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