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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 6

A new approach to a theorem of Eng

Hasan Arslan
Sayfa
1679–1680
Yayın Tarihi
2022-10-18
DOI
—
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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.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Coxeter groups · descent algebras · Poincaré polynomial

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.

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Bu Makaleye Atıf Yap

Arslan, H. (2022). A new approach to a theorem of Eng. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1679–1680. https://ajindex.com/articles/529448

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Kaynakça (7)

  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.