Permutation enumeration, symmetric functions and the Gessel-Reutenauer Theorem

Postgraduate Thesis uoadl:2768119 445 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2018-06-14
Year:
2018
Author:
Mavrothalassitis Stavros
Supervisors info:
Αθανασιάδης Χρήστος , Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Μαλιάκας Μιχάλης , Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Ντόκας Ιωάννης ,Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Απαρίθμηση Μεταθέσεων, Συμμετρικές Συναρτήσεις και το Θεώρημα Gessel-Reutenauer
Languages:
Greek
Translated title:
Permutation enumeration, symmetric functions and the Gessel-Reutenauer Theorem
Summary:
The subject of this paper is permutation enumeration. In particular, we would like to count the number of permutations with given cycle structure and descent set. The main result is the Gessel-Reutenauer Teorem, which states that the number of permutation having descent set D and cycle structure λ is equal to the scalar product of two characters of the symmetric group. In the first two chapters we introduce the basic concepts along with elements of the theory of symmetric functions. In the third chapter we prove the Gessel-Reutenauer Theorem and we present one of its applications.
Main subject category:
Science
Keywords:
Combinatorics, permutation enumeration, cycle structure, descent set, symmetric functions, quasi-symmetric functions, ribbon Schur functions, Lie representation, Foulkes representation
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
16
Number of pages:
37
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