6,029 research outputs found

    Editor’s note

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    This Special Issue, entitled Algebraic Combinatorics and Applications, of the Journal of Algebra, Combinatorics, Discrete Structures, and Applications, contains selected papers submitted by conference participants at the "Algebraic Combinatorics and Applications: The First Annual Kliakhandler Conference", Houghton, Michigan, USA, August 26 - 30, 2015, as well as two additional papers submitted in response to our call for papers. The conference took place on the campus of Michigan Technological University, and was attended by 43 researchers and graduate and postdoctoral students from USA, Canada, Croatia, Japan, South Africa, and Turkey. Funding for the conference was provided by a generous gift of Igor Kliakhandler, and a grant from the National Science Foundation. The conference brought together researchers and students interested in combinatorics and its applications, to learn about the latest developments, and explore different visions for future work and collaborations. Over thirty talks were presented on various topics from combinatorial designs, graphs, finite geometry, and their applications to error-correcting codes, network coding, information security, quantum computing, DNA codes, mobile communications, and tournament scheduling. The current Special Issue contains papers on covering arrays and their applications, group divisible designs, automorphism groups of combinatorial designs, covering number of permutation groups, tournaments, large sets of geometric designs, partitions, quasi-symmetric functions, resolvable Steiner systems, and weak isometries of Hamming spaces

    Implementing Brouwer's database of strongly regular graphs

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    Andries Brouwer maintains a public database of existence results for strongly regular graphs on n1300n\leq 1300 vertices. We implemented most of the infinite families of graphs listed there in the open-source software Sagemath, as well as provided constructions of the "sporadic" cases, to obtain a graph for each set of parameters with known examples. Besides providing a convenient way to verify these existence results from the actual graphs, it also extends the database to higher values of nn.Comment: 18 pages, LaTe

    The State-of-the-Art of Set Visualization

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    Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net
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