Brian W. Curtin

Associate Professor

CONTACT

Office: CMC 318
Phone: (813) 974-4929
Email

EDUCATION

Ph.D., Mathematics, University of Wisconsin, Madison, 1996
B.A. summa cum laude, Mathematics & Physics, Ripon College, 1991

RESEARCH

The algebraic combinatorics of distance-regular graphs, spin models, Bose-Mesner algebras, and planar algebras.

RECENT PUBLICATIONS

  1. B. Curtin and G.R. Pourgholi, An Euler totient sum inequality. J. Number Theory 163 (2016), 101–113.
  2. H. Alnajjar and B. Curtin, Leonard triples from the equitable basis of \(\mathrm{sl}(2)\). Linear Algebra Appl. 482 (2015), 47–54.
  3. B. Curtin, E. Salter and D. Stone, Lucas’ hyperbolas for Fibonacci vectors. Fibonacci Quarterly 50 (2012), 51–57.

Publications

B. Curtin and G.R. Pourgholi,
An Euler totient inequality
J. Number Theory 163 (2016) 101-113.
 | 
MR3459563 | doi:/10.1016/j.jnt.2015.11.012
B. Curtin, G.R. Pourgholi, and H. Yousefi-Azari,
On the punctured power graph of a finite group
Australas. J. Combin. 62 (2015) 1-7.

MR3337172
H. Alnajjar and B. Curtin,
Leonard triples from the equitable basis of sl(2).
Linear Algebra Appl. 482 (2015), 47-54.

MR3365264 | doi:10.1016/j.laa.2015.05.018
B. Curtin and G.R. Pourgholi,
A group sum inequality and its application to power graphs
Bull. Aust. Math. Soc. 90(3) (2014), 418-426.
 | 
MR3270756 | doi:10.1017/S0004972714000434
B. Curtin and G.R. Pourgholi,
Edge-maximality of power graphs of finite cyclic groups
J. Algebraic Combin. 40(2) (2014), 313-330.
 | 
MR3239288 | doi:10.1007/s10801-013-0490-5
H. Alnajjar and B. Curtin,
A bidiagonal and tridiagonal linear map with respect to eigenbases of equitable basis of sl(2).
Linear Multilinear Algebra 61 (2013), no. 12, 1668-1674.

MR3175393 | doi:10.1080/03081087.2012.753597
B. Curtin, E. Salter Michael, D. Stone,
Lucas' hyperbolas for Fibonacci vectors
Fibonacci Quarterly 50(1) (2012), 51-57.

MR2892010
H. Alnajjar and B. Curtin,
Leonard pairs from the equitable basis of sl(2).
Electron. J. Linear Algebra 20 (2010), 490-505.

MR2735969 | doi:10.13001/1081-3810.1389
B. Curtin and I. Daqqa,
The subconstituent algebra of strongly regular graphs associated with a Latin square
Designs, Codes, and Cryptography 52(3) (2009) 263-274.

MR2506727 | doi:10.1007/s10623-009-9281-3
B. Curtin and I. Daqqa,
The subconstituent algebra of a Latin square
European Journal of Combinatorics 30(2) (2009), 447-457.

MR2489277 | doi:10.1016/j.ejc.2008.04.003
B. Curtin,
Hyper-duality of Type II Bose-Mesner algebras
Journal of Applied Algebra and Discrete Structures 6 (2008) 1-11.

MR2428225
B. Curtin,
Inheritence of hyper-duality in imprimitive Bose-Mesner algebras
Discrete Mathematics 308(15) (2008), 3003-3017.

MR2413877 | doi:10.1016/j.disc.2007.08.025
H. Alnajjar and B. Curtin,
A bilinear form for tridiagonal pairs of q-Serre type.
Linear Algebra Appl. 428 (2008), no. 11-12, 2688-2698.

MR2416580 | doi:10.1016/j.laa.2007.12.015
B. Curtin, E. Salter Michael, D. Stone,
Some Formulae for the Fibonacci numbers
Fibonacci Quarterly 45(2) (2007), 171-180.

MR2407770
B. Curtin,
Spin Leonard pairs.
Ramanujan J. 13 (2007), no. 1-3, 319-332.

MR2281169 | doi:10.1007/s11139-006-0255-z
B. Curtin,
Modular Leonard triples.
Linear Algebra Appl. 424 (2007), no. 2-3, 510-539.

MR2329491 | doi:10.1016/j.laa.2007.02.024
B. Curtin,
Algebraic characterizations of graph regularity conditions
Designs, Codes and Cryptography 34(2) (2005) 241-248.

MR2128333 | doi: 10.1007/s10623-004-4857-4
H. Alnajjar and B. Curtin,
A family of tridiagonal pairs related to the quantum affine algebra Uq(sl(2)).
Electron. J. Linear Algebra 13 (2005), 1-9.

MR2148891| doi:10.13001/1081-3810.1147
B. Curtin and K. Nomura,
1-Homogeneous, pseudo 1-homogeneous, and 1-thin distance-regular graphs
J. Combin. Theory Ser. B 93(2) (2005), 279-302.

MR2117939 | doi:10.1016/j.jctb.2004.10.003
H. Alnajjar and B. Curtin,
A family of tridiagonal pairs.
Linear Algebra Appl. 390 (2004), 369-384.

MR2083667| doi:10.1016/j.laa.2004.05.003
B. Curtin and K. Nomura,
Homogeneity of a distance-regular graph which support a spin model
J. Alg. Combin. 19 (2004), no. 3, 257-272.

MR2071473 | doi:10.1023/B:JACO.0000030702.58352.f7
B. Curtin,
Some planar algebras related to graphs
Pacific Journal of Mathematics 209 (2003), no. 2, 231-248.

MR1978369 | doi:10.2140/pjm.2003.209.231
B. Curtin,
The Terwilliger algebra of a 2-homogeneous bipartite distance-regular graph
J. Combin. Theory Ser. B. 81 (2001), no. 1, 125-141.

MR1809430 | doi:10.1006/jctb.2000.2002
B. Curtin and K. Nomura,
Spin models and strongly hyper-self-dual Bose-Mesner algebras
J. Alg. Combin. 13 (2001), no. 2, 173-186.

MR1826951 | doi:10.1023/A:1011297515395
B. Curtin and K. Nomura,
Distance-regular graphs related to the quantum enveloping algebra of sl(2).
Journal of Algebraic Combinatorics 12 (2000), no. 1, 25-36.

MR1791444 | doi:10.1023/A:1008707417118
B. Curtin,
Almost 2-homogeneous bipartite distance-regular graphs
European J. Combin. 21 (2000), no. 7, 865-876.

MR1787900 | doi:10.1006/eujc.2000.0399
B. Curtin and K. Nomura,
Some formulas for spin models on distance-regular graphs
J. Combin. Theory Ser. B 75 (1999), 206--236.

MR1676889 | doi:10.1006/jctb.1998.1876
B. Curtin,
Distance-regular graphs which support a spin model are thin
Discr. Math. 197--198 (1999), 205-216.

MR1674863 | doi:10.1016/S0012-365X(99)90065-1
B. Curtin,
The local structure of a bipartite distance-regular graph.
European Journal of Combinatorics 20 (1999), no. 8, 739-758.

MR1730822 | doi:10.1006/eujc.1999.0307
B. Curtin,
Bipartite distance-regular graphs. I.
Graphs and Combinatorics 15 (1999), no. 2, 143-158.

MR1701778 | doi:10.1007/s003730050049
B. Curtin,
Bipartite distance-regular graphs. II.
Graphs and Combinatorics 15 (1999), no. 4, 377-391.

MR1735086 | doi:10.1007/s003730050072
B. Curtin,
2-Homogeneous bipartite distance-regular graphs
Discr. Math. 187 (1998) 39-70.

MR1630676 | doi:10.1016/S0012-365X(97)00226-4