- Algebraic Combinatorics; in particular, theory of
association schemes; schemes are combinatorial configurations which
may be viewed as generalized groups and generalized distance-regular
graphs. The theory provides a foundation of an algebraic approach to
error-correcting codes and combinatorial designs.
- Interests also lie in other combinatorial and
algebraic objects, such as, combinatorial designs, distance-regular
graphs, codes, matrix theory, extremal set theory, cryptography,
classical groups, permutation groups, loops, partially ordered sets,
group characters and representations.
- Recent work:
-- A family of designs over finite fields (joint with Grant Bowling, Kavi Duvvoori and Robert Lazar).
-- Combinatorial direct sums of Terwilliger algebras and coherent configurations
(joint with Bangteng Xu and Shenglin Zhou). (in preparation).
-- Normally regular digraphs, association schemes, and related
combinatorial structures (joint with Leif Jorgensen, Gareth Jones and
Mikhail Klin). Seminaire Lotharingien
de Combinatoire, vol. 71 (2014), 39pp. (on-line version available at http://www.mat.univie.ac.at/~slc).
-- Links between orthogonal arrays, association schemes and partial
geometric designs (joint with Katy Nowak and Oktay Olmez). Submitted
(available in arXiv.1501.01684) 22 pp.
-- Partial geometric difference families. Journal of Combinatorial Designs (joint with Katy Nowak and
Oktay Olmez). To appear. (on-line version available in the journal website:
DOI 10.1002/jcd.21416.) 20 pp.
-- Some families of directed strongly regular graphs obtained from
certain finite incidence structures (joint with Oktay Olmez). Graphs and Combinatorics, 30 (2014), no.6, 1529--1549.
-- Directed strongly regular graphs from one-and-half designs
(joint with Andries Brouwer and Oktay Olmez). European Journal of Combinatorics, 33 (2012), pp. 1174--1177.
Fall 2015 (For course
information go to Blackboard)
(Name: degree conferred or
anticipated dates, current affiliation, dissertation title)
Nowak: May 2015, Pacific Northwest National Laboratory (Partial geometric
designs and difference families)
- Oktay Olmez: May 2012, Ankara University,
Faculty of Science (On highly regular digraphs)
- Gargi Bhattacharyya: May 2008, Occidental
College, CA (Terwilliger algebras of wreath products of association
- Juhyung Kim: August 2005, Wonkwang
University, Korea (Classification of small-class association schemes
obtained from certain combinatorial objects) with Dr. Ling Long
- Mandi Maxwell: May 2005, Trinity College in
Chicago (Almost perfect nonlinear functions and related combinatorial
structures) with Dr. Clifford Bergman
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