Beginning with the outside influences, it can be said that the recent development of combinatorics is somewhat of a cinderella story. It used to be looked down on by “mainstream” mathematicians as being somehow less respectable than other areas, in spite of many services rendered to both pure and applied mathematics. Then along came the prince of computer science with its many mathematical problems and needs — and it was combinatorics that best fitted the glass slipper held out.
A. Björner and R. Stanley, A Combinatorial Miscellany, 2010.
My main scientific interests lie at the interplay between combinatorics on words, numeration systems, formal languages, and automata theory. I also play with number theory on the side. I like questions related to Pascal’s triangle, binomial coefficients, words complexity functions, distinguished families of infinite words (e.g., automatic, synchronized, regular, morphic, Lyndon, Nyldon, Sturmian, episturmian), all Cobham’s theorems, topics related to factorizations of words (e.g., Ziv-Lempel, Crochemore, string attractors), and pattern avoidance (e.g., fractional powers). And I love sequences of integers, especially the OEIS!
2020 Mathematics Subject Classification: 05A05, 05A10, 05A15, 11A63, 11A67, 11B39, 11B57, 11B65, 11B85, 11J70, 11K16, 28A78, 28A80, 41A60, 68Q45, 68Q70, 68R01, 68R05, 68R15, 68V15, 68V20, 94A45