Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Moustakas Vassileios-Dionysios
Supervisors info:
Χρήστος Α. Αθανασιάδης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Η κατανομή του Euler επί των αυτοαντίστροφων στοιχείων της υπεροκταεδρικής ομάδας
Translated title:
The Eulerian distribution on the involutions of the hyperoctahedral group
Summary:
The subject of study is the Eulerian distribution on the involutions of the symmetric and the hyperoctahedral group.
We compute the generating function of the B-Eulerian polynomial on signed involutions using the theory of symmetric and quasisymmetric functions.
Then we prove the unimodality of this polynomial. The proof follows that of Victor J.W. Guo and Jiang Zeng (2006) for the unimodality of the
Eulerian distribution on involutions. Furthermore, using elements of representation theory we calculate two formulas of Christos A. Athanasiadis
for the Eulerian polynomial on involutions and the B-Eulerian polynomial on signed involutions.
Main subject category:
Science
Other subject categories:
Algebra
Keywords:
involutions, descent number, uimodality, Eulerian polynomial, hyperoctahedral group, B-Eulerian polynomial, symmetric functions, quasisymmetric functions, representation theory, generating function
