Area of Catalan paths on a checkerboard

Abstract: It is known that the area of all Catalan paths of length is equal to , which coincides with the number of inversions of all 321-avoiding permutations of length . In this paper, a bijection between the two sets is established. Meanwhile, a number of interesting bijective results that pave the way to the required bijection are presented. [Copyright &y& Elsevier]