Restricted growth functions, rank row matchings of partition lattices, and q-Stirling numbers

✍ Scribed by Stephen C Milne

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 1012 KB
• Volume: 43
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(82)90032-9

✦ Synopsis

In this paper we use restricted growth functions to give a direct algebraic description of the incidence relations of the lattice of partitions of an n-set that is independent of the partitions themselves. This description of the incidence relations not only gives new information about rank row matchings of partition lattices but is of independent interest since every finite lattice is a sublattice of some partition lattice. As a further application of restricted growth functions we show how the polynomials in q known as q-Stirling numbers of the second kind may be viewed as generating functions.