Generalized Ordered Set Partitions
MTMT : 31337443
Megjelenés dátuma : 2020
Folyóirat címe : Australasian Journal of Combinatorics
Évfolyam : 77
Szám : 2
Oldalszám : 157-179
Dokumentum típusa : folyóiratcikk
Kulcsszó : set partitions, Lah numbers, ombinatorial sequence, exponential generating function, recurrence relations, combinatorial identities, Riordan arrays, families of posets, Természettudományok, Természettudományok/Matematika- és számítástudományok
Absztrakt :
In this paper, we consider ordered set partitions obtained by imposing conditions on the size of the lists, and such that the first r elements are in distinct blocks, respectively. We introduce a generalization of the Lah numbers. For this new combinatorial sequence we derive its exponential generating function, some recurrence relations, and combinatorial identities. We prove and present results using combinatorial arguments, generating functions, the symbolic method and Riordan arrays. For some specific cases we provide a combinatorial interpretation for the inverse matrix of the generalized Lah numbers by means of two families of posets.