Colin Defant

About Me

I am a 4th-year Ph.D. student in the Princeton Mathematics department. I graduated with a B.S. in mathematics from the University of Florida in 2017. During the summers of 2017, 2018, 2019, and 2020, I worked as an advisor at the University of Minnesota Duluth Mathematics REU Program



All of my papers are available on

47. C. Defant and K. Zheng, Stack-sorting with consecutive-pattern-avoiding stacks. To appear in Adv. Appl. Math., (2021).

46. C. Defant, Fertility monotonicity and average complexity of the stack-sorting map. European J. Combin., 93 (2021), 17 pages.

45. C. Defant, Highly sorted permutations and Bell numbers. Enumer. Combin. Appl.1 (2021), 7 pages.

44. C. Defant, Enumeration of stack-sorting preimages via a decomposition lemma. To appear in Discrete Math. Theor. Comput. Sci., (2021).

43. A. Berger and C. Defant, On anti-powers in aperiodic recurrent words. Adv. Appl. Math., 121 (2020), 11 pages.

42. C. Defant and J. Propp, Quantifying noninvertibility in discrete dynamical systems. Electron. J. Combin., 2(2020), 22 pages.

41. C. Defant, Polyurethane toggles. Electron. J. Combin., 27 (2020), 16 pages.

40. A. Burcroff and C. Defant, Pattern-avoiding permutation powers. Discrete Math., 343 (2020), 11 pages.


39. C. Defant, N. Kravitz, and A. Sah, Supertrees. Electron. J. Combin., 27 (2020), 26 pages.

38. C. Defant, M. Engen, and J. A. Miller, Stack-sorting, set partitions, and Lassalle's sequence. J. Combin. Theory Ser. A, 175 (2020), 24 pages.

37. C. Defant, Stack-sorting preimages of permutation classes. Sém. Lothar. Combin., 82B (2020), 41 pages.

36. C. Defant, Catalan intervals and uniquely sorted permutations. J. Combin. Theory Ser. A, 174 (2020), 43 pages.

35. C. Defant and N. Kravitz, Stack-sorting for words. Australas. J. Combin., 77 (2020), 51-68

34. C. Defant, Counting 3-Stack-Sortable Permutations. J. Combin. Theory Ser. A, 172 (2020), 26 pages.

33. C. Defant, Fertility, strong fertility, and postorder Wilf equivalence. Australas. J. Combin., 76 (2020), 149-182.

32. N. Alon and C. Defant, Isoperimetry, stability, and irredundance in direct products. Discrete Math., 343 (2020), 19 pages.

31. C. Defant, Descents in t-sorted permutations. J. Comb., 11 (2020), 527-548.

30. C. Defant, Fertility numbers. J. Comb., 11 (2020), 511-526.

29. S. Cho, J. Cummings, C. Defant, and C. Sonneborn, An anti-Ramsey problem concerning complete bipartite graphs. AKCE Int. J. Graphs. Comb. (2019), In press.

28. C. Defant, Proofs of conjectures about pattern-avoiding linear extensions. Discrete Math. Theor. Comput. Sci., 21 (2019), #16, 9 pages.

27. C. Defant, Enumerating cliques in direct product graphs. J. Comb., 11 (2019), 351-358.

26. A. Adeniran, S. Butler, C. Defant, Y. Gao, P. E. Harris, C. Hettle, Q. Liang, H. Nam, and A. Volk, On the genus of a quotient of a numerical semigroup. Semigroup Forum, 98 (2019), 690-700.

25. C. Defant and S. Iyer, Domination and upper domination of direct product graphs. Discrete Math., 341 (2018), 2742-2752.

24. C. Defant, Flexible toggles and symmetric invertible asynchronous elementary cellular automata. Discrete Math., 341 (2018), 2367-2379.

23. C. Defant, Connected components of complex divisor functions. J. Number Theory, 190 (2018), 56-71.

22. C. Defant, Ranges of unitary divisor functions. Integers, 18 (2018), #A15, 10 pages.

21.  K. Alladi and C. Defant, Revisiting the Riemann zeta function at positive even integers. Int. J. Number Theory14 (2018), 1849-1856.

20. C. Defant, Poset pattern-avoidance problems posed by Yakoubov. J. Comb., 9 (2017), 233-257.

19. C. Defant, Anti-power prefixes of the Thue-Morse word. Electron. J. Combin., 24 (2017), Paper #P1.32, 17 pages.

18. C. Defant, Preimages under the stack-sorting algorithm. Graphs Combin., 33 (2017), 103-122.

Link Here.

17. C. Defant, Postorder preimages. Discrete Math. Theor. Comput. Sci., 19 (2017), #3, 15 pages.

16. C. Defant, On Schemmel nontotient numbers. J. Comb. Number Theory, 8 (2016), 233-239.

15. C. Defant, Upper bounds for Stern's diatomic sequence and related sequences. Electron. J. Combin., 23 (2016) , Paper #P4.8, 47 pages.

14. C. Defant, Unitary Cayley graphs of Dedekind domain quotients. AKCE Int. J. Graphs Comb., 13 (2016), 65-75.

13. C. Defant, Complex divisor functions. Analysis, Geometry and Number Theory, 1 (2016), 22-48.

12. C. Defant, Binary codes and period-2 orbits of sequential dynamical systems. Discrete Math. Theor. Comput. Sci., 19 (2015), #10, 12 pages.

11. C. Defant, On 2-powerfully perfect numbers in three quadratic rings. Notes on Number Theory and Discrete Mathematics, 23 (2017), 1-11.

10. C. Defant, A note about iterated arithmetic functions. Miskolc Math. Notes16 (2015), 763-767.

9. C. Defant, On arithmetic functions related to iterates of the Schemmel totient functions. J. Integer Seq. 18 (2015), Article 15.2.1.

8. C. Defant, On the density of ranges of generalized divisor functions with restricted domains. Unif. Distrib. Theory, 10 (2015), 19-33.

7. C. Defant, Unitary multiperfect numbers in certain quadratic rings. Int. J. Math. Comput. Sci., 10 (2015), 127-138.

6. C. Defant, On the density of ranges of generalized divisor functions. Notes on Number Theory and Discrete Mathematics, 21 (2015), 80-87.

5. C. Defant, On ranges of variants of the divisor functions that are dense. Int. J. Number Theory, 11 (2015), 1905-1912.

4. C. Defant, On sparsely Schemmel totient numbers. Integers, 15 (2015), #A18, 13 pages.

3. C. Defant, An arithmetic function arising from the Dedekind $\psi$ function. Math. J. Okayama Univ., 59 (2017), 81-92.

2. C. Defant, Multiperfect numbers in certain quadratic rings. Int. J. Math Comput. Sci., 9 (2014), 49-61.

1. C. Defant, An extension of the abundancy index to certain quadratic rings. Int. J. Math Comput. Sci., 9 (2014), 63-82.

Submitted Papers

8. C. Defant. Fertilitopes. Submitted.

7. C. Defant and S. Hopkins, Symmetry of Narayana numbers and rowvacuation of root posets. Submitted.

6. C. Defant, A. Elvey Price, and A. J. Guttmann, Asymptotics of 3-stack-sortable permutations. Submitted.

5. N. Alon, C. Defant, and N. Kravitz, Typical and extremal aspects of friends-and-strangers graphs. Submitted.

4. C. Defant and N. Kravitz, Friends and strangers walking on graphs. Submitted.

3. C. Defant and Noah Kravitz, Promotion sorting. Submitted.

2. C. Defant, Troupes, cumulants, and stack-sorting. Submitted. 

1. C. Defant, Motzkin intervals and valid hook configurations. Submitted.

My interests are primarily in enumerative and algebraic combinatorics. A large portion of my work in combinatorics concerns a specific function called the stack-sorting map. In order to understand this function, I've developed a theory of new combinatorial objects that I call valid hook configurations. I've also explored these new objects in their own right. I especially enjoy finding other parts of combinatorics that are connected with stack-sorting and valid hook configurations. For example, I have found that valid hook configurations show up in a very simple yet surprising combinatorial formula in free probability theory; this has allowed me to use free probability in order to understand the stack-sorting map and to use a generalization of stack-sorting to derive new combinatorial facts about free and classical cumulants.    

Some Talks


These are some simple short songs that I made in 2014 for a computer game that a team of undergraduates at Cornell made.

Song 1 - Unknown Artist
Song 2 - Colin Defant
Song 3 - Colin Defant
Song 4 - Colin Defant
Song 5 - Colin Defant