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|dc.description.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
5 also includes some work we have done towards answering Question 14.3
of  for interval building sets.||en_AU|
|dc.publisher||University of Sydney.||en_AU|
|dc.title||Gamma-polynomials of flag homology spheres||en_AU|
|dc.type.pubtype||Doctor of Philosophy Ph.D.||en_AU|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
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