Frequency permutation arrays

Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n=m lambda and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency lambda, such that the Hamming distance between any distinct x,y in T is at least d. Such arrays have potential applications in powerline communication. In this paper, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.Comment: To appear in Journal of Combinatorial Design

Experimental Designs and Combinatorial Systems Associated with Latin Squares and Sets of Mutually Orthogonal Latin Squares

14 pages, 1 article*Experimental Designs and Combinatorial Systems Associated with Latin Squares and Sets of Mutually Orthogonal Latin Squares* (Hedayat, A.; Shrikhande, S. S.) 14 page

An evaluation of planarity of the spatial QRS loop by three dimensional vectorcardiography: its emergence and loss

Aims: To objectively characterize and mathematically justify the observation that vectorcardiographic QRS loops in normal individuals are more planar than those from patients with ST elevation myocardial infarction (STEMI). Methods: Vectorcardiograms (VCGs) were constructed from three simultaneously recorded quasi-orthogonal leads, I, aVF and V2 (sampled at 1000 samples/s). The planarity of these QRS loops was determined by fitting a surface to each loop. Goodness of fit was expressed in numerical terms. Results: 15 healthy individuals aged 35–65 years (73% male) and 15 patients aged 45–70 years (80% male) with diagnosed acute STEMI were recruited. The spatial-QRS loop was found to lie in a plane in normal controls. In STEMI patients, this planarity was lost. Calculation of goodness of fit supported these visual observations. Conclusions: The degree of planarity of the VCG loop can differentiate healthy individuals from patients with STEMI. This observation is compatible with our basic understanding of the electrophysiology of the human heart