The problem of relevant enumeration with pattern-avoiding permutations is a significant topic in enumerative combinatorics and has wide applications in physics,chemistry,and computer science.This paper summarizes the ...The problem of relevant enumeration with pattern-avoiding permutations is a significant topic in enumerative combinatorics and has wide applications in physics,chemistry,and computer science.This paper summarizes the relevant conclusions of the enumeration of pattern-avoiding permutations on the nelement symmetric group Sn,alternating permutations,Dumont permutations,Ballot permutations,and inversion sequences.It also introduces relevant research results on avoiding vincular patterns and barred patterns in S_(n).展开更多
文摘The problem of relevant enumeration with pattern-avoiding permutations is a significant topic in enumerative combinatorics and has wide applications in physics,chemistry,and computer science.This paper summarizes the relevant conclusions of the enumeration of pattern-avoiding permutations on the nelement symmetric group Sn,alternating permutations,Dumont permutations,Ballot permutations,and inversion sequences.It also introduces relevant research results on avoiding vincular patterns and barred patterns in S_(n).
