Abstract
We present estimations of the roots of r-Dowling, r-Lah and r-Dowling–Lah polynomials. It is known that these polynomials have simple, real and non-positive roots. We give bounds for them and we also compute the real magnitude of the roots via computational methods.
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Benoumhani, M.: On some numbers related to Whitney numbers of Dowling lattices. Adv. in Appl. Math. 19, 106–116 (1997)
Benoumhani, M.: Log-concavity of Whitney numbers of Dowling lattices. Adv. in Appl. Math. 22, 186–189 (1999)
Bóna, M., Mező, I.: Real zeros and partitions without singleton blocks. European J. Combin. 51, 500–510 (2016)
Broder, A.Z.: The \(r\)-Stirling numbers. Discrete Math. 49, 241–259 (1984)
Carlitz, L.: Weighted Stirling numbers of the first and second kind I. Fibonacci Quart. 18, 147–162 (1980)
Cheon, G.-S., Jung, J.-H.: \(r\)-Whitney numbers of Dowling lattices. Discrete Math. 312, 2337–2348 (2012)
Corcino, R.B., Corcino, C.B., Aldema, R.: Asymptotic normality of the \((r,\beta )\)-Stirling numbers. Ars Combin. 81, 81–96 (2006)
Dowling, T.A.: A class of geometric lattices based on finite groups. J. Combin. Theory Ser. B 14, 61–86 (1973)
E. Gyimesi, The \(r\)-Dowling–Lah polynomials, submitted
E. Gyimesi and G. Nyul, New combinatorial interpretations of \(r\)-Whitney and \(r\)-Whitney–Lah numbers, Discrete Appl. Math., 255 (2019), 222–233.
Gyimesi, E., Nyul, G.: A comprehensive study of \(r\)-Dowling polynomials. Aequationes Math. 92, 515–527 (2018)
Laguerre, E.: Sur une méthode pour obtenir par approximation les racines d'une équation algébrique qui a toutes ses racines réelles. Nouvelles Annales de Mathématiques 19(161–171), 193–202 (1880)
Merris, R.: The \(p\)-Stirling numbers. Turkish J. Math. 24, 379–399 (2000)
Mező, I.: On the maximum of \(r\)-Stirling numbers. Adv. in Appl. Math. 41, 293–306 (2008)
Mező, I.: A new formula for the Bernoulli polynomials. Results Math. 58, 329–335 (2010)
I. Mező, The \(r\)-Bell numbers, J. Integer Sequences, 14 (2011), Article 11.1.1
Mező, I., Corcino, R.B.: The estimation of the zeros of the Bell and \(r\)-Bell polynomials. Appl. Math. Comput. 250, 727–732 (2015)
Nyul, G., Rácz, G.: The \(r\)-Lah numbers. Discrete Math. 338, 1660–1666 (2015)
G. Nyul and G. Rácz, Sums of \(r\)-Lah numbers and \(r\)-Lah polynomials, submitted
G. Pólya and G. Szegő, Problems and Theorems in Analysis, I, Classics in Mathematics, vol. 193, Springer (Berlin–Heidelberg, 1998)
Samuelson, P.A.: How deviant can you be? J. Amer. Statist. Assoc. 63, 1522–1525 (1968)
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This research was supported by the ÚNKP-18-3 New National Excellence Program of the Ministry of Human Capacities.
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Rácz, G. On the magnitude of the roots of some well-known enumerative polynomials. Acta Math. Hungar. 159, 257–264 (2019). https://doi.org/10.1007/s10474-019-00925-6
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DOI: https://doi.org/10.1007/s10474-019-00925-6