Two Special Types of Parking Functions Related to Catalan Number and Fine Number

Abstract

We introduce two special types of parking function V-parking function and Lambda-parking function which are inspired by the unimodal sequence Then we prove the suprising facts that the number of V-parking functions are Catalan numbers and the number of Lambda-parking functions are Fine numbers (In appendix A we verify that the diagonal sums of Catalan triangle are Fine numbers by giving bijections )

Date of Award	2019
Original language	English
Supervisor	Po-Yi Huang (Supervisor)