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Log-concavity of Whitney numbers of Dowling lattices. (English) Zbl 0918.05003
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.

MSC:
05A15Exact enumeration problems, generating functions
06C10Semimodular lattices, geometric lattices
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Full Text: DOI
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) · Zbl 0283.05001
[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) · 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) · Zbl 0608.05001
[8] Stanley, R.: Log-concave and unimodal sequence in algebra. Combinatorics and geometry (1989) · 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