TY  - JOUR
T1  - A new approach to a theorem of Eng
AU  - Arslan, Hasan
PY  - 2021
DA  - December
DO  - 10.15672/hujms.900705
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1679
EP  - 1680
VL  - 50
IS  - 6
LA  - en
AB  - 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.
KW  - Coxeter groups
KW  - descent algebras
KW  - Poincaré polynomial
KW  - the longest
element
KW  - $q=-1$ phenomenon
CR  - [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.
CR  - [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.
CR  - [3] O. Eng, Quotients of Poincaré polynomials evaluated at -1, J. Algebraic Combin. 13
(1), 29-40, 2001.
CR  - [4] J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Ad-
vanced Mathematics 29, Cambridge University Press, 1990.
CR  - [5] V. Reiner, Note on a theorem of Eng, Ann. Comb. 6 (1), 117-118, 2002.
CR  - [6] V. Reiner, D. Stanton and D. White, The cyclic sieving phenomenon, J. Combin.
Theory Ser. A 108 (1), 17-50, 2004.
CR  - [7] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41
(2), 255-264, 1976.
UR  - https://doi.org/10.15672/hujms.900705
L1  - https://dergipark.org.tr/en/download/article-file/1652929
ER  -