Brenti, Francesco; Carnevale, Angela Proof of a conjecture of Klopsch-Voll on Weyl groups of type \(A\). (English) Zbl 1368.05007 Trans. Am. Math. Soc. 369, No. 10, 7531-7547 (2017). Summary: We prove a conjecture of Klopsch-Voll on the signed generating function of a new statistic on the quotients of the symmetric groups. As a consequence of our results we also prove a conjecture of Stasinski-Voll in type \( B\). Cited in 1 ReviewCited in 9 Documents MSC: 05A15 Exact enumeration problems, generating functions 05E15 Combinatorial aspects of groups and algebras (MSC2010) 20F55 Reflection and Coxeter groups (group-theoretic aspects) 20B30 Symmetric groups Keywords:signed generating function PDF BibTeX XML Cite \textit{F. Brenti} and \textit{A. Carnevale}, Trans. Am. Math. Soc. 369, No. 10, 7531--7547 (2017; Zbl 1368.05007) Full Text: DOI OpenURL References: [1] Bj\"orner, Anders; Brenti, Francesco, Combinatorics of Coxeter groups, Graduate Texts in Mathematics 231, xiv+363 pp. (2005), Springer, New York · Zbl 1110.05001 [2] Humphreys, James E., Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29, xii+204 pp. (1990), Cambridge University Press, Cambridge · Zbl 0725.20028 [3] Klopsch, Benjamin; Voll, Christopher, Igusa-type functions associated to finite formed spaces and their functional equations, Trans. Amer. Math. Soc., 361, 8, 4405-4436 (2009) · Zbl 1229.05288 [4] Lan A. Landesman, Proof of Stasinski and Voll’s hyperoctahedral group conjecture, arXiv:1408.7105 [math.CO]. · Zbl 1406.05010 [5] Stanley, Richard P., Enumerative combinatorics. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, xiv+306 pp. (1986), Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA · Zbl 0608.05001 [6] Stanley, Richard P., Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics 62, xii+581 pp. (1999), Cambridge University Press, Cambridge · Zbl 0928.05001 [7] Stasinski, Alexander; Voll, Christopher, A new statistic on the hyperoctahedral groups, Electron. J. Combin., 20, 3, Paper 50, 23 pp. pp. (2013) · Zbl 1295.05038 [8] Stasinski, A.; Voll, C., Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type \(B\), Amer. J. Math., 136, 2, 501-550 (2014) · Zbl 1286.11140 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.