- 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:
-- 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.
2015 (For course information go to
- Introduction to Number Theory (Math 350) (Class
Meeting Time & Place: MWF 1:10 -- 2:00 PM. Carver 118)
- Enumerative Combinatorics
and Ordered Sets (Math 606) (MWF 11:00 – 11:50 AM, Carver 196)
- Honors Research (Math 290H) in Graphs and Network
- Research (Math 699) in Algebraic Combinatorics
Ph.D. Students Supervised
(Name: degree conferred or anticipated dates, current
affiliation, dissertation title)
Moss: 2016—2017, ISU (Schematic
orthogonal arrays and codes)
Nowak: May 2015, ISU (Difference sets
and difference families)
- Oktay Olmez: May 2012, Ankara University,
Faculty of Science (On highly regular digraphs)
Bhattacharyya: May 2008, Occidental College,
CA (Terwilliger algebras of wreath products of
Kim: August 2005, Wonkwang University, Korea (Classification of
small-class association schemes obtained from certain combinatorial
objects) with Dr. Ling Long
Maxwell: May 2005, Trinity College in
Chicago (Almost perfect nonlinear functions and related combinatorial structures)
with Dr. Clifford Bergman
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