Multi-preference Parking-functions, Combinatorial Statistics and Their Applications

One of the aims of the project is to extend results on matching statistics on partitions to more involved combinatorial structures such as labeled trees, parking functions and labeled graphs. The other aim is to generalize standard parking functions by allowing tuples as preferences. The results of the project may help in improving rescheduling algorithms that are used heavily in business problems such as runway assignments to flights during sudden delays. Specially, for Qatar rescheduling of events such as outdoor sports or flights assigned to a runway may be necessary time to time due to sand storms or other reasons. The area may be of particular interest considering the soccer world cup in 2022. The other results on counting of statistics are helpful in many areas of computer science and biology. In particular, it is used in understanding of protein folding. Qatar is investing in molecular biology and our results in this area may offer a possibility of collaboration among various groups.