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Archive : Discrete Mathematics

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Gene Fiorini, Muhlenberg College Gene Fiorini, Muhlenberg College Ewing 336Title: Challenges of Researching Integer Sequences Using the OEIS <br></br> Abstract: Sequences play an important role in number theory, combinatorics and discrete mathematics, among many other fields. They enumerate objects in sets and define relationships among items or properties shared between them. Integer sequences have inspired mathematicians for centuries. Likewise, they also inspire computer scientists. The quest to compute new, larger terms in important infinite sequences is harnessing the power of computing and promoting the use of new paradigms in distributed and cloud computing as well as Big Data. Current examples include the "Great Internet Mersenne Prime Search" to find Mersenne primes (sequence A000668 in OEIS) and MicrosoftÂ’s challenge to discover non-Mersenne or "lost" primes (sequence A138837). By gathering sequences and a wealth of information about them together in a common database, the OEIS (Online Encyclopedia of Integer Sequences), established by Neil Sloane, provides the mathematically curious an invaluable resource with which to explore. This talk presents new results on integer sequences associated with the Catalan triangle as well as discussing some interesting sequences found in the OEIS and its role in stimulating new research. 9/13/2017 1:00:00 PM9/13/2017 2:00:00 PMFalse
Jun Zhang, Capital Normal University, Beijing (visiting University of Oklahoma)Jun Zhang, Capital Normal University, Beijing (visiting University of Oklahoma)Ewing 336Title: An Efficient Version of the Bombieri-Vaaler Lemma <br><br>Abstract: In their celebrated paper "On Siegel's Lemma", Bombieri and Vaaler found an upper bound on the height of integer solutions of systems of linear Diophantine equations. Calculating the bound directly, however, requires exponential time. In this talk, we present the bound in a different form that can be computed in polynomial time. We also give an elementary (and arguably simpler) proof for the bound. (Joint work with Qi Cheng.) 9/6/2017 1:00:00 PM9/6/2017 2:00:00 PMFalse
Bernardo Rodrigues, School of Mathematics, Statistics and Computer Science at University of KwaZulu-Natal, South AfricaBernardo Rodrigues, School of Mathematics, Statistics and Computer Science at University of KwaZulu-Natal, South AfricaEwing 336Title: On linear codes with complementary duals obtained from permutation modules of finite groups6/13/2017 6:00:00 PM6/13/2017 7:00:00 PMFalse
Ferdinand Ihringer, University of ReginaFerdinand Ihringer, University of ReginaEWG 336Title: Ovoids in Generalizes Quadrangles Abstract: A generalized quadrangle (GQ) of order ( s, t ) consists of a set of points P and a set of lines L such that (1) each line contains exactly s + 1 points, (2) each point lies in exactly t + 1 lines, (3) a more technical condition that prevents triangles, but guarantees the existence of quadrangles. The point graph of a GQ is strongly regular. A coclique of size 1 + st of the point graph is called an ovoid . A coclique of smaller size is called a partial ovoid . In the talk we will discuss the existence of ovoids in GQs and, if they do not exist, bounds on the size of partial ovoids.4/26/2017 3:00:00 PM4/26/2017 4:00:00 PMFalse

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