Pronouns: he/him
Fall 2023 conversation hours (office hours): Mon 3-4, Thu 11:30-12:30, Fri 10-11
Hi! I am an Assistant Professor of Mathematics, teaching 2-3 courses each semester and researching enumerative and algebraic combinatorics. I began at Cal State LA in Fall 2022. 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!
A guide on improving your grade in a math class, which I wrote for my calculus students in Fall 2023
Here is my list of publications, works in progress, and unpublished papers:
- J. M. Troyka, "New generalizations of the Foulkes Conjecture on q-binomial coefficients", in progress.
- M. Omar and J. M. Troyka, "Growth rates of permutations with a given descent word", in progress.
- S. Elizalde, J. M. Troyka, and Y. Zhuang, “Statistics on clusters and r-Stirling permutations”, to appear in J. Comb. (2023).
- 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.
- 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.