|Title:||Gamma-polynomials of flag homology spheres|
|Publisher:||University of Sydney.|
|Abstract:||Chapter 1 contains the main definitions used in this thesis. It also includes some basic theory relating to these fundamental concepts, along with examples. Chapter 1 includes an original result, Theorem 1.5.4, answering a question of Postnikov-Reiner-Williams, which characterises the normal fans of nestohedra. Chapter 2 contains the content of the paper , of which Theorem 2.0.6 is the main result. As mentioned,  shows that the Nevo and Petersen conjecture holds for simplicial complexes in sd(Σd−1). . Chapter 3 includes the content of the paper , where we show that the Nevo and Petersen conjecture holds for the dual simplicial complexes to nestohedra in Theorem 3.0.4. Chapter 4 contains the content of the paper  in which we prove Conjecture 0.0.4 in Theorem 4.1.2 by showing that tree shifts lower the γ-polynomial of graph-associahedra. Chapter 4 also includes Theorem 4.2.1, which shows that flossing moves also lower the γ-polynomial of graph-associahedra. In Chapter 5 we include smaller results that have been made. This chapter includes a result proving Gal’s conjecture for edge subdivisions of the order complexes of Gorenstein* complexes, and shows that this result can be attributed to the work of Athanasiadis in . Chapter viii INTRODUCTION 5 also includes some work we have done towards answering Question 14.3 of  for interval building sets.|
|Type of Work:||PhD Doctorate|
|Type of Publication:||Doctor of Philosophy Ph.D.|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
|Aisbett_N_Thesis_2013.pdf||578.36 kB||Adobe PDF|
Items in Sydney eScholarship Repository are protected by copyright, with all rights reserved, unless otherwise indicated.