| Pattern avoidance on combinatorial objects was raised by H.Wilf in the 1980s,which has attracted much attention.The main problems of this research direction are enumerating pat-tern avoiding combinatorial objects and establishing the relationship with other combinatorial objects.In this paper,we are mainly concerned with the enumeration of two classes of pattern avoiding combinatorial objects.To this end,we aim to establish bijections between these ob-jects.In chapter 1,we introduce the research background,preliminaries and our main results.In chapter 2,we provide a proof of a conjecture posed by Martinez and Savage,which asserts that inversion sequences e=(e1,e2,…,en)containing no three indices i<j<k such that ei≥ej,ej ≥ek and ei>ek are counted by Baxter numbers.Moreover,we show that two new classes of pattern avoiding inversion sequences are also counted by Baxter numbers.In chapter 3,we mainly give two proofs of a conjecture posed by Selig et al.which asserts that EW-tableaux of size n with k columns containing a 0 is counted by Eulerian number A(n,k). |
