We study some polynomials arising from Whitney numbers of the second kind of Dowling lattices. Special cases of our results include well-known identities involving Stirling numbers of the second kind. The main technique used is essentially due to Rota.
Log-Concavity of Whitney Numbers of Dowling Lattices
β Scribed by Moussa Benoumhani
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 40 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0196-8858
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β¦ Synopsis
We prove that the generating polynomial of Whitney numbers of the second kind of Dowling lattices has only real zeros.
π SIMILAR VOLUMES
For k l we construct an injection from the set of pairs of matchings in a given graph G of sizes l&1 and k+1 into the set of pairs of matchings in G of sizes l and k. This provides a combinatorial proof of the log-concavity of the sequence of matching numbers of a graph. Besides, this injection impl
We extend a well-known relationship between the representation of the symmetric group on the homology of the partition lattice and the free Lie algebra to Dowling lattices.