Unit:
Τομέας Άλγεβρας ΓεωμετρίαςLibrary of the School of Science
Author:
Σαββίδου Χριστίνα
Dissertation committee:
Χρήστος Α. Αθανασιάδης Καθηγητής (Επιβλέπων) , Παναγιώτης Παπάζογλου Καθηγητής , Ολυμπία Ταλέλλη Καθηγήτρια
Original Title:
Βαρυκεντρικές υποδιαιρέσεις, σμήνη και απαρίθμηση μεταθέσεων
Translated title:
Barycentric subdivisions, clusters and permutation enumeration
Summary:
The local h-polynomial of a subdivision of the simplex was defined by Stanley.
He also proved that the local h-polynomial of the barycentric subdivision of
the simplex is equal to the derangement polynomial, that enumerates
permutations without fixed points according to the number of excedances. As an
analogue, another barycentric subdivision is studied and results on the
enumeration of singed permutations without fixed points are derived. Moreover,
it is proved that the local h-polynomial is γ-nonnegative for the cluster
subdivision and combinatorial interpretations are given in terms of noncrossing
partitions for the classical root systems. Finally, the tranformation of the
cubical h-vectors of a cubical complex under cubical barycentric subdivision is
studied.
Keywords:
Subdivisions, Local h-vector, Local γ-vector, Clusters, Permutations
