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Proof of a conjecture of Klopsch-Voll on Weyl groups of type $$A$$. (English) Zbl 1368.05007
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 $$B$$.

##### 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
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##### 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
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