Let S be a subset of the positive integers, and let σ be a permutation of S. We say that σ is a k-avoiding permutation of S if σ does not contain any k-term AP as a subsequence. Similarly, the set S is said to be k-avoidable if there exists a k-avoiding permutation of S.

the recent years have witnessed an increasing attention to the methods of multiple attribute decision making in solving the problems of the real world due to their shorter time of calculation and easy application. one of these methods is the ‘permutation method’ which has a strong logic in connection with ranking issues, but when the number of alternatives increases, solving problems through th...

This paper describes a new concept for the parallel implementation of functional languages on a network of processors. The implementation uses a special variant of annotated graph reduction 3]. The main features of it are the following: We employ active waiting 6], to avoid complicated runtime data structures. We use a global address space, and a random distribution of the graph nodes over the ...

the group $2^6{{}^{cdot}} g_2(2)$ is a maximal subgroup of the rudvalis group $ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. in this paper, we construct the character table of the group $2^6{{}^{cdot}} g_2(2)$ by using the technique of fischer-clifford matrices.

Given n items, a parallel algorithm for generating the n! permutations is presented. This algorithm is designed to run on a linear array consisting of n identical processing elements (PEs for short). These PEs are numbered and referred to as PE(i) for 1 < i < n. Each PE is responsible for producing one component of each permutation. Every PE(i) contains six registers, namely: C(i), T(i), K(i), ...

This paper addresses the problem of parallel transposition of large out-of-core arrays. Although algorithms for out-of-core matrix transposition have been widely studied, previously proposed algorithms have sought to minimize the number of I/O operations and the inmemory permutation time. We propose an algorithm that directly targets the improvement of overall transposition time. The I/O charac...

I/O libraries such as PANDA and DRA use blocked layouts for efficient access to disk-resident multi-dimensional arrays, with the shape of the blocks being chosen to match the expected access pattern of the array. Sometimes, different applications, or different phases of the same application, have very different access patterns for an array. In such situations, an array’s blocked layout represen...

Determining the sequence-recognition properties of DNA-binding proteins and small molecules remains a major challenge. To address this need, we have developed a high-throughput approach that provides a comprehensive profile of the binding properties of DNA-binding molecules. The approach is based on displaying every permutation of a duplex DNA sequence (up to 10 positional variants) on a microf...