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Let S n denote the symmetric group on [n] = {1,. .. , n}. A family I ⊆ S n is intersecting if any two elements of I have at least one common entry. It is known that the only intersecting families of maximal size in S n are the cosets of point stabilizers. We show that, under mild restrictions, analogous results hold for the alternating group and the direct… (More)

Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable… (More)

We consider integer matrices N t (h) whose rows are indexed by the t-subsets of an n-set and whose columns are all images of a particular column h under the symmetric group S n. Earlier work has determined a diagonal form for N t (h) when h has at least t 'isolated vertices' and the results were applied to the binary case of a zero-sum Ramsey-type problem… (More)

Since 2007, the Telescope Array (TA) experiment, based in Utah, USA, has been observing ultra high energy cosmic rays to understand their origins. The experiment involves a surface detector (SD) array and three fluores-cence detector (FD) stations. FD stations, installed surrounding the SD array, measure the air fluorescence light emitted from extensive air… (More)

Let G be a subgraph of a complete bipartite graph K n,n. Let N (G) be a 0-1 incidence matrix with edges of K n,n against images of G under the automorphism group of K n,n. A diagonal form of N (G) is found for every G, and whether the row space of N (G) over Z p contains the vector of all 1's is determined. This reproves Caro and Yuster's results on… (More)

- T Abu-Zayyad, R Aida, M Allen, R Anderson, R Azuma, E Barcikowski +138 others
- 2013

We measure the spectrum of cosmic rays with energies greater than 10 18.2 eV with the Fluorescence Detectors (FDs) and the Surface Detectors (SDs) of the Telescope Array Experiment using the data taken in our first 2.3-year observation A hybrid air shower reconstruction technique is employed to improve accuracies in determination of arrival directions and… (More)

We consider integer matrices N t whose rows are indexed by the t-subsets of an n-set and whose columns are all distinct images of a particular column under the symmetric group S n. Examples include matrices in the association algebras of the Johnson schemes. Three related problems are addressed. What is the Smith normal form (or a diagonal form) for N t and… (More)

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