Benoumhani, Moussa Log-concavity of Whitney numbers of Dowling lattices. (English) Zbl 0918.05003 Adv. Appl. Math. 22, No. 2, 186-189 (1999). This paper shows that the generating polynomial of Whitney numbers of the Dowling lattices has only real roots. This gives a new proof (through a result of Newton) that these Whitney numbers form strictly log-concave sequences. Reviewer: P.L.Erdős (Budapest) Cited in 20 Documents MSC: 05A15 Exact enumeration problems, generating functions 06C10 Semimodular lattices, geometric lattices Keywords:Dowling lattice; geometric lattice; log-concave; generating function; Stirling numbers of the second kind; Whitney numbers PDFBibTeX XMLCite \textit{M. Benoumhani}, Adv. Appl. Math. 22, No. 2, 186--189 (1999; Zbl 0918.05003) Full Text: DOI Link References: [1] Brenti, F., Unimodal, log-concave, and Pólya frequency sequences, Mem. Amer. Math. Soc., 413 (1989) · Zbl 0697.05011 [2] Comtet, L., Advanced Combinatorics (1974), Reidel: Reidel Boston [3] Damiani, T. E.; D’Antona, O.; Regonati, F., Whitney numbers of some geometric lattices, J. Combin. Theory Ser. A, 65, 11-25 (1994) · Zbl 0793.05037 [4] Dowling, T. A., A class of geometric lattices based on finite groups, J. Combin. Theory Ser. B, 14, 61-86 (1973) · Zbl 0247.05019 [5] Hardy, G. H.; Littlewood, J. E.; Pólya, G., Inequalities (1952), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0047.05302 [6] Harper, L., Stirling behaviour is asymptotically normal, Ann. Math. Stat., 38, 401-414 (1967) · Zbl 0154.43703 [7] Stanley, R., Enumerative Combinatorics (1986), Wadsworth and Brooks/Cole: Wadsworth and Brooks/Cole Monterey [8] Stanley, R., Log-Concave and Unimodal Sequence in Algebra. Log-Concave and Unimodal Sequence in Algebra, Combinatorics and Geometry (1989), Annals of the Academy of Science of New York, p. 500-535 · Zbl 0792.05008 [9] Stonesifer, S. J.R., Logarithmic concavity for a class of geometric lattices, J. Combin. Theory Ser. A, 216-218 (1975) · Zbl 0312.05019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.