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.
journal article page (subscription) | Video abstract
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.
Journal table of contents
MR3337172
H. Alnajjar and B. Curtin,
Leonard triples from the equitable basis of sl(2).
Linear Algebra Appl. 482 (2015), 47-54.
journal article page
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.
journal article page (subscription) | ArXiv:1311.2983
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.
journal article page (subscription) | ArXiv:1311.2984
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.
journal article page
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.
Journal table of contents (subscription)
MR2892010
H. Alnajjar and B. Curtin,
Leonard pairs from the equitable basis of sl(2).
Electron. J. Linear Algebra 20 (2010), 490-505.
journal article page
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.
journal article page (subscription)
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.
journal article page
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.
Journal table of contents (no article link)
MR2428225
B. Curtin,
Inheritence of hyper-duality in imprimitive Bose-Mesner algebras
Discrete Mathematics 308(15) (2008), 3003-3017.
journal article page
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.
journal article page
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.
Journal table of contents
MR2407770
B. Curtin,
Spin Leonard pairs.
Ramanujan J. 13 (2007), no. 1-3, 319-332.
journal article page (subscription)
MR2281169 | doi:10.1007/s11139-006-0255-z
B. Curtin,
Modular Leonard triples.
Linear Algebra Appl. 424 (2007), no. 2-3, 510-539.
journal article page
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.
journal article page
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.
journal article page
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.
journal article page
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.
journal article page
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.
journal article page (subscription)
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.
journal article page
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.
journal article page
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.
journal article page (subscription)
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.
journal article page (subscription)
MR1791444 | doi:10.1023/A:1008707417118
B. Curtin,
Almost 2-homogeneous bipartite distance-regular graphs
European J. Combin. 21 (2000), no. 7, 865-876.
journal article page
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.
journal article page
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.
journal article page
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.
journal article page
MR1730822 | doi:10.1006/eujc.1999.0307
B. Curtin,
Bipartite distance-regular graphs. I.
Graphs and Combinatorics 15 (1999), no. 2, 143-158.
journal article page (subscription)
MR1701778 | doi:10.1007/s003730050049
B. Curtin,
Bipartite distance-regular graphs. II.
Graphs and Combinatorics 15 (1999), no. 4, 377-391.
journal article page (subscription)
MR1735086 | doi:10.1007/s003730050072
B. Curtin,
2-Homogeneous bipartite distance-regular graphs
Discr. Math. 187 (1998) 39-70.
journal article page
MR1630676 | doi:10.1016/S0012-365X(97)00226-4