Sung-Yell Song

scription: Description: Description: Description: Description: Description:

  Associate Professor
  Director of Graduate Education
  Department of Mathematics
  442 Carver Hall
  Iowa State University
  Ames, IA 50011
Telephone: (515)-294-5866
  Fax: (515)-294-5454

  Office Hours (Spring 2019):

 MWF: 1:10 - 2:00 PM;
  T: 12:10 - 2:00 PM
  (or by appointment)



Research Interests

  • 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, codes, matrix theory, extremal set theory, classical groups, permutation groups, loops, partially ordered sets, group characters and representations.
  • Recent work:

-- A class of partial geometric designs coming from classical sympletic geometry (joint with Robert Lazar). in progress

-- Graphs that are cospectral for the distance Laplacian (joint with Boris Brimkov, Ken Duna, Leslie Hogben, Kate Lorenzen, Carolyn Reinhart and Mark Yarrow). arXiv:1812.05734v1 [math.CO] (Dec. 2018) 18pp.

-- Investigations on association schemes with elementary abelian thin residue (joint with Kijung Kim and Bangteng Xu). Discrete Math 340 (2017), 2813-2821.

-- On the Wiener index, distance cospectrality and transmission regular graphs (joint with A. Abiad, B. Brimkov, A. Erey, L. Leshock, X. Martinez-Rivera, S. O and J. Wiiliford). Discrete Applied Math 230 (2017), 1-10. (arXiv:1609.06911 in \underline{})

-- Combinatorial extensions of Terwilliger algebras and wreath products of association schemes (joint with Bangteng Xu and Shenglin Zhou). Discrete Math 340 (2017), 892--905.

-- Normally regular digraphs, association schemes, and related combinatorial structures (joint with Leif Jorgensen, Gareth Jones and Mikhail Klin). Seminaire Lotharingien de Combinatoire, vol. 71 (2013/14), 39pp. (on-line version available at

-- A family of partial geometric designs from three-class association schemes (joint with Katy Nowak and Oktay Olmez). Journal of Combinatorial Designs 24 (2016), no. 12, 533--552.

-- Partial geometric difference families. Journal of Combinatorial Designs (joint with Katy Nowak and Oktay Olmez). 24 (2016), 112--131.

-- 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.

Publication List


Teaching Schedule

Spring 2019 (For course information go to Canvas)

  • Intermediate Abstract Algebra (Math 403X/503X) (Class Meeting Time (and Place): MWF 2:10 -- 3:00 PM. (Carver 294))
  • Graduate Student Orientation (Math 592) (W 4:10 -- 5:00 PM. (Carver 174))
  • Creative Component (Math 599) in Design Theory
  • Graduate Research (Math 699) in Algebraic Combinatorics

Courses Taught


Ph.D. Students

(Name: degree conferred dates, current affiliation, dissertation theme or title)

  • Nate Benjamin: Current, ISU (Highly structured graphs and coherent configurations)
  • Ted Tranel: Current, ISU (Group divisible designs with multiple resolutions)
  • Robert Lazar: Dec 2017, ISU (Association schemes and designs in symplectic vector spaces over finite fields)
  • Darren Rasberry: May 2017, Mercy College of Health Sciences (On minimal support solutions of underdetermined systems of linear equations) Dissertation supervised by Dr. Irvin Hentzel
  • Kathleen 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 schemes)
  • Juhyung Kim: August 2005, Wonkwang University, Korea (Classification of small-class association schemes obtained from certain combinatorial objects) Co-supervised with Dr. Ling Long
  • Mandi Maxwell: May 2005, Trinity College in Chicago (Almost perfect nonlinear functions and related combinatorial structures) Co-supervised with Dr. Clifford Bergman

Curriculum Vitae


Links to



This page updated on 01/30/2019 12:00PM

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