Hi! I am an Assistant Professor of Mathematics, teaching 2-3 courses each semester and researching enumerative and algebraic combinatorics. I study permutations, symmetric functions, and graph enumeration. I earned my BA in mathematics in 2013 at Carleton College (Minnesota), and I earned my PhD in mathematics at Dartmouth College in 2018 where my advisor was Sergi Elizalde. After that, I spent two years as a postdoctoral visitor at York University (Toronto) and collaborated on research with Neal Madras, followed by two years as a visiting assistant professor at Davidson College (North Carolina) where I got valuable teaching experience and worked on combinatorics research with colleague Yan Zhuang. I'm excited to be here at Cal State LA!
Here is my list of publications, works in progress, and unpublished papers:
- J. M. Troyka, "An asymptotic version of the generalized Foulkes conjecture", in progress.
- J. M. Troyka, “Growth rates of permutations with a given descent set”, in progress.
- J. M. Troyka and Y. Zhuang, “Permutation clusters and generalized Stirling permutations”, in progress.
- J. M. Troyka and Y. Zhuang, “Fibonacci numbers, consecutive patterns, and inverse peaks”, Adv. in Appl. Math. 141 (2022): 102406 (free version on arXiv).
- J. J. Fang, Z. Hamaker, and J. M. Troyka, “On pattern avoidance in matchings and involutions”, Electron. J. Combin. 29 (2022): #P1.39.
- N. Madras and J. M. Troyka, “Bounded affine permutations II. Avoidance of decreasing patterns”, Ann. Comb. 25 (2021): 1007–1048.
- N. Madras and J. M. Troyka, “Bounded affine permutations I. Pattern avoidance and enumeration”, Discrete Math. Theor. Comput. Sci. 22(2) (2021): #1.
- J. M. Troyka, “Period mimicry: A note on the (–1)-evaluation of the peak polynomials”, arXiv:1907.06681 (2019).
- J. M. Troyka, “Split graphs: Combinatorial species and asymptotics”, Electron. J. Combin. 26 (2019): #P2.42.
- J. M. Troyka, “On the centrosymmetric permutations in a class”, Australas. J. Combin. 74 (2019): 423–442.
- S. Elizalde and J. M. Troyka, “Exact and asymptotic enumeration of cyclic permutations according to descent set”, J. Combin. Theory Ser. A 165 (2019): 360–391 (free version on arXiv).
- A. Hardt, P. McNeely, T. Phan, and J. M. Troyka, “Combinatorial species and graph enumeration” (undergraduate senior thesis), arXiv:1312.0542 (2013). A concise expository introduction to the theory of combinatorial species.
- A. Hardt and J. M. Troyka, “Restricted symmetric signed permutations”, Pure Math. Appl. 23 (2012): 179–217.