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A new approach to a theorem of Eng

Yıl 2021, Cilt: 50 Sayı: 6, 1679 - 1680, 14.12.2021

Hasan Arslan

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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.

Yıl 2021, Cilt: 50 Sayı: 6, 1679 - 1680, 14.12.2021

Hasan Arslan

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

Öz

Kaynakça

  • [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.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Hasan Arslan 0000-0002-0430-8737

Yayımlanma Tarihi 14 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 6

Kaynak Göster

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. Aralık 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, sy. 6 (Aralık 2021): 1679-80. https://doi.org/10.15672/hujms.900705.
EndNote Arslan H (01 Aralık 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, c. 50, sy. 6, ss. 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 (Aralık 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, c. 50, sy. 6, 2021, ss. 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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