António Carlos Henriques Guedes de Oliveira's Annual Report
Year:
Brief description of the research activities:
Rui Duarte and I were able to count the parking functions with center of a given length. This envolves a number of bijections between different structures and different statistics and presents a perhaps unexpected complexity. We published a local pre-print and an ArXiv one, and submitted it in mid-July. It was the end of a project more than a year long. So far, we did not receive any feedback.
Starting in September, and now ready for pre-printing, we prepared another manuscript in a close direction, where we extended results common to the Shi and the Ish arrangements to new arrangements "between" these two arrangements.
I started to write a book with a course in Elementary Geometry (more precisely, on compass-and-ruler constructions, from a didactic viewpoint).