Research

Here is a list of my publications:

• 1.  Transitive actions and purely periodic $N$-expansions, J Number Theory 283(2026), 1--14

  2. On 2025 and Other Torn Numbers, Amer. Math. Monthly (2025), 1--7.

  3. Dynamics of the Fibonacci Order of Appearance Map, Fibonacci Quart. (2025), 1-12. Joint with S. Miller et al. 

  4. Harmonious sequences in groups with a unique involution, Combin. Theory 5(2025), no. 3, Article 65556.  Joint with L. de Wolf.

  5. Doubly sequencable groups, J. Combin. Designs 32(2024), no. 7, 371-387. 

  6. On a Cyclic Inequality Related to Chebyshev Polynomials, Involve 17(2024), no. 3, 519--530. Joint with H. Shen. 

  7. Upper Bound Residues of the Fibonacci Sequence Modulo Primes, Fibonacci Quart. 60(2022), no. 1, 48--51. 

  8. The Distribution of Fibonacci Numbers Modulo Primes, Amer. Math. Monthly, 129(2022), no. 1,  75--79. Joint with S. Cambrea. 

  9. Permutations with a distinct divisor property, Internat. Electron. J. Algebra, 29(2021), 1-14. Joint with N.A. Krylov. 

  10. On Sets Closed Under the Cross Product and a Property of the Octahedron, Amer. Math. Monthly, 127(2020), 151-158. 

  11. Complete Generalized Fibonacci Sequences Modulo Primes, Moscow J. Comb. Number Theory, 9-1(2020), 1-15. Joint with N.A. Krylov.

  12. Cyclic composition operators on separable locally compact metric spaces, Topology Appl. 258(2019), 126-141. 

  13. On the subgroup generated by solutions of Pell's equation, J. Number Theory 194(2019), 356-371. Joint with E. Covill and N.A. Krylov.

  14. A note on polynomial sequences modulo integers, J. Integer Sequences 22(2019), Article 19.1.1.

  15. Projective partitions of vector spaces, Electron. J. Linear Algebra 32(2017), 125--130.

  16. Loxodromes on hypersurfaces of revolution, Involve 10(2017), no. 3, 465–472. Joint with J. Blackwood & A. Dukehart. 

  17. The correlation numerical range and trace-positive complex polynomials, Oper. Matrices 10(2016), no. 3, 625-630. Joint with E. Bashwinger & J. Bannon.

  18. Cycle double covers of infinite planar graphs, Discuss. Math. Graph Theory 36(2016), no. 3, 523--544.

  19. On transitive polynomials modulo integers, Notes Number Theory Discrete Math. 22(2016), no. 2, 23--35. Joint with G.Rusak.

  20. Dynamics of semigroups of linear fractional transformations, Dyn. Syst. 29(2014), no. 4,  439--450. 

  21. Hypercyclic and topologically transitive semigroups of composition operators, Topology Appl. 164(2014), 105--112.

  22. Maximally transitive semigroups of nxn matrices, J. Math. Anal. Appl. 401(2013), 743--753. 

  23. A Collatz-type conjecture on the set of rational numbers, J. Number Theory 132(2012), no. 11, 2582--2594.

  24. Dense 2-generator subsemigroups of 2x2 matrices, J. Math. Anal. Appl. 387(2012), 103--113.

  25. Semigroups of matrices with dense orbits, Dyn. Syst. 26(2011), no. 3, 235--243.

  26. Topologically transitive semigroup actions of real linear fractional transformations, J. Math. Anal. Appl. 368(2010), 587--603.

  27. Rigidity of conformally compact manifolds with the round sphere as the conformal infinity, Adv. Math. 224(2010), 525--538. Joint with S. Dutta.

  28. On a property of plane curves, J. Math. Anal. Appl. 361(2010), 332--337.

  29. Convergence of Ricci flow on R^2 to flat space, J. Geom. Anal. 19(2009), 809--816. Joint with J. Isenberg.

  30. Chord theorems on graphs, Proc. Amer. Math. Soc. 137(2009), 553--562.

  31. A generalization of Dirichlet approximation theorem for the affine actions on real line, J. Number Theory 128(2008), no. 5, 1146--1156.

  32. Dirichlet problem on locally finite graphs, Discrete Appl. Math. 155(2007), no. 18, 2496--2506.

  33. A new arrangement inequality, J. Inequal. Pure Appl. Math. 7(2006), no. 5, Article 162.