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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 \( B\).

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
Full Text: DOI
[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, \em Proof of Stasinski and Voll’s hyperoctahedral group conjecture, arXiv:1408.7105 [math.CO]. · Zbl 1406.05010
[5] \bibStaEC1book author=Stanley, Richard P., title=Enumerative combinatorics. Vol. I, series=The Wadsworth & Brooks/Cole Mathematics Series, pages=xiv+306, publisher=Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, date=1986, doi=10.1007/978-1-4615-9763-6, isbn=0-534-06546-5, review=\MR 847717,
[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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