Proof of a conjecture of Klopsch-Voll on Weyl groups of type $A$
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- by Francesco Brenti and Angela Carnevale PDF
- Trans. Amer. Math. Soc. 369 (2017), 7531-7547 Request permission
Abstract:
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 $B$.References
- Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005. MR 2133266
- James E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990. MR 1066460, DOI 10.1017/CBO9780511623646
- Benjamin Klopsch and Christopher Voll, Igusa-type functions associated to finite formed spaces and their functional equations, Trans. Amer. Math. Soc. 361 (2009), no. 8, 4405–4436. MR 2500892, DOI 10.1090/S0002-9947-09-04671-6
- A. Landesman, Proof of Stasinski and Voll’s hyperoctahedral group conjecture, arXiv:1408.7105 [math.CO].
- Richard P. Stanley, Enumerative combinatorics. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986. With a foreword by Gian-Carlo Rota. MR 847717, DOI 10.1007/978-1-4615-9763-6
- Richard P. Stanley, Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999. With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin. MR 1676282, DOI 10.1017/CBO9780511609589
- Alexander Stasinski and Christopher Voll, A new statistic on the hyperoctahedral groups, Electron. J. Combin. 20 (2013), no. 3, Paper 50, 23. MR 3118958, DOI 10.37236/3242
- A. Stasinski and C. Voll, Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type $B$, Amer. J. Math. 136 (2014), no. 2, 501–550. MR 3188068, DOI 10.1353/ajm.2014.0010
Additional Information
- Francesco Brenti
- Affiliation: Dipartimento di Matematica, Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy
- MR Author ID: 215806
- Email: brenti@mat.uniroma2.it
- Angela Carnevale
- Affiliation: Dipartimento di Matematica, Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy
- Address at time of publication: Fakultat für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany
- Email: acarneva1@math.uni-bielefeld.de
- Received by editor(s): September 4, 2014
- Received by editor(s) in revised form: December 29, 2016
- Published electronically: May 31, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 7531-7547
- MSC (2010): Primary 05A15; Secondary 05E15, 20F55
- DOI: https://doi.org/10.1090/tran/7197
- MathSciNet review: 3683117