In this paper we consider the enumeration of subsets of the set, say Dm, of those Dyck paths of arbitrary length with maximum peak height equal to m and having a strictly increasing sequence of peak height （as one go...In this paper we consider the enumeration of subsets of the set, say Dm, of those Dyck paths of arbitrary length with maximum peak height equal to m and having a strictly increasing sequence of peak height （as one goes along the path）. Bijections and the methods of generating trees together with those of Riordan arrays are used to enumerate these subsets, resulting in many combinatorial structures counted by such well-known sequences as the Catalan nos., Narayana nos., Motzkin nos., Fibonacci nos., Schroeder nos., and the unsigned Stirling numbers of the first kind. In particular, we give two configurations which do not appear in Stanley＇s well-known list of Catalan structures.展开更多
This paper gives a unified approach to Hsu's two classes of extended GSN pairs in the setting of Hsu-Riordan partial monoid which is a generalization of Shapiro's Riordan group, and moreover Hsu-Wang transfer ...This paper gives a unified approach to Hsu's two classes of extended GSN pairs in the setting of Hsu-Riordan partial monoid which is a generalization of Shapiro's Riordan group, and moreover Hsu-Wang transfer theorem, Drown-Sprugnoli transfer formula and generalized Brown transfer lemma which display some transfer methods of different kinds of Hsu-Riordau arrays and identities respectively.展开更多
文摘In this paper we consider the enumeration of subsets of the set, say Dm, of those Dyck paths of arbitrary length with maximum peak height equal to m and having a strictly increasing sequence of peak height （as one goes along the path）. Bijections and the methods of generating trees together with those of Riordan arrays are used to enumerate these subsets, resulting in many combinatorial structures counted by such well-known sequences as the Catalan nos., Narayana nos., Motzkin nos., Fibonacci nos., Schroeder nos., and the unsigned Stirling numbers of the first kind. In particular, we give two configurations which do not appear in Stanley＇s well-known list of Catalan structures.
文摘This paper gives a unified approach to Hsu's two classes of extended GSN pairs in the setting of Hsu-Riordan partial monoid which is a generalization of Shapiro's Riordan group, and moreover Hsu-Wang transfer theorem, Drown-Sprugnoli transfer formula and generalized Brown transfer lemma which display some transfer methods of different kinds of Hsu-Riordau arrays and identities respectively.
