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A new approach to a theorem of Eng

Year 2021, Volume: 50 Issue: 6, 1679 - 1680, 14.12.2021

Hasan Arslan

https://doi.org/10.15672/hujms.900705

Abstract

The main aim of this work is to give a case-free algebraic proof for a theorem of Eng on the Poincaré polynomial of parabolic quotients of finite Coxeter groups evaluated at -1.

Keywords

Coxeter groups descent algebras Poincaré polynomial the longest element $q=-1$ phenomenon

References

  • [1] D. Blessenohl, C. Hohlweg and M. Schocker, A symmetry of the descent algebra of a finite Coxeter group, Adv. Math. 193 (2), 416-437, 2005.
  • [2] C.W. Curtis and I. Reiner, Methods of Representation Theory with Applications to Finite Groups and Orders Vol. II, John Wiley and Sons, 1987.
  • [3] O. Eng, Quotients of Poincaré polynomials evaluated at -1, J. Algebraic Combin. 13 (1), 29-40, 2001.
  • [4] J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Ad- vanced Mathematics 29, Cambridge University Press, 1990.
  • [5] V. Reiner, Note on a theorem of Eng, Ann. Comb. 6 (1), 117-118, 2002.
  • [6] V. Reiner, D. Stanton and D. White, The cyclic sieving phenomenon, J. Combin. Theory Ser. A 108 (1), 17-50, 2004.
  • [7] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (2), 255-264, 1976.

Year 2021, Volume: 50 Issue: 6, 1679 - 1680, 14.12.2021

Hasan Arslan

https://doi.org/10.15672/hujms.900705

Abstract

References

  • [1] D. Blessenohl, C. Hohlweg and M. Schocker, A symmetry of the descent algebra of a finite Coxeter group, Adv. Math. 193 (2), 416-437, 2005.
  • [2] C.W. Curtis and I. Reiner, Methods of Representation Theory with Applications to Finite Groups and Orders Vol. II, John Wiley and Sons, 1987.
  • [3] O. Eng, Quotients of Poincaré polynomials evaluated at -1, J. Algebraic Combin. 13 (1), 29-40, 2001.
  • [4] J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Ad- vanced Mathematics 29, Cambridge University Press, 1990.
  • [5] V. Reiner, Note on a theorem of Eng, Ann. Comb. 6 (1), 117-118, 2002.
  • [6] V. Reiner, D. Stanton and D. White, The cyclic sieving phenomenon, J. Combin. Theory Ser. A 108 (1), 17-50, 2004.
  • [7] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (2), 255-264, 1976.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Hasan Arslan 0000-0002-0430-8737

Publication Date December 14, 2021
Published in Issue Year 2021 Volume: 50 Issue: 6

Cite

APA Arslan, H. (2021). A new approach to a theorem of Eng. Hacettepe Journal of Mathematics and Statistics, 50(6), 1679-1680. https://doi.org/10.15672/hujms.900705
AMA Arslan H. A new approach to a theorem of Eng. Hacettepe Journal of Mathematics and Statistics. December 2021;50(6):1679-1680. doi:10.15672/hujms.900705
Chicago Arslan, Hasan. “A New Approach to a Theorem of Eng”. Hacettepe Journal of Mathematics and Statistics 50, no. 6 (December 2021): 1679-80. https://doi.org/10.15672/hujms.900705.
EndNote Arslan H (December 1, 2021) A new approach to a theorem of Eng. Hacettepe Journal of Mathematics and Statistics 50 6 1679–1680.
IEEE H. Arslan, “A new approach to a theorem of Eng”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 6, pp. 1679–1680, 2021, doi: 10.15672/hujms.900705.
ISNAD Arslan, Hasan. “A New Approach to a Theorem of Eng”. Hacettepe Journal of Mathematics and Statistics 50/6 (December 2021), 1679-1680. https://doi.org/10.15672/hujms.900705.
JAMA Arslan H. A new approach to a theorem of Eng. Hacettepe Journal of Mathematics and Statistics. 2021;50:1679–1680.
MLA Arslan, Hasan. “A New Approach to a Theorem of Eng”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 6, 2021, pp. 1679-80, doi:10.15672/hujms.900705.
Vancouver Arslan H. A new approach to a theorem of Eng. Hacettepe Journal of Mathematics and Statistics. 2021;50(6):1679-80.

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