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Dissertation_Acan.pdf (657.7 KB)
ETD Abstract Container
Abstract Header
An Enumerative-Probabilistic Study of Chord Diagrams
Author Info
Acan, Huseyin
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1373310487
Abstract Details
Year and Degree
2013, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
In this thesis, we study various enumerative and probabilistic problems concerning chord diagrams, permutations, chord intersection graphs, and permutation graphs. Among the enumerative results, we find the number of tree permutation graphs on
n
vertices, the number of forests with
n
vertices and
m
edges in both chord intersection graphs and permutation graphs, and the number of unicyclic connected graphs on
n
vertices in chord intersection graphs and permutation graphs. For the probabilistic results related to chord diagrams and chord intersection graphs, we consider
C
n
, a chord diagram chosen uniformly at random from all chord diagrams with
n
chords, and
G
C
n
, the intersection graph of
C
n
. In
G
C
n
, we find the limiting distribution of the degree of a chord scaled by
n
, and find upper and lower bounds for both the clique number and the independence number of
G
C
n
. We extend in several directions a result of Flajolet and Noy about the structure of
C
n
. We find the distribution of the size of the
k
-core for a fixed
k
, and the asymptotic size of the set of vertices outside of the
k
-core as
k
tends to infinity slowly enough. We define two evolution processes, each of which gives
C
n
at step
n
, and we show that they are equivalent. In random permutations, we consider the permutation
σ
(n,m)
, which is chosen uniformly at random from all permutations of
n
with
m
inversions, and study the probability that it is indecomposable. We show that this probability increases with
m
by finding an evolution process similar to the Erdos-Renyi graph process. We find the threshold value of
m
for the indecomposability of
σ
(n,m)
(equivalently the connectedness of
G
σ
(n,m)
). Finally, we study the sizes of the largest and the smallest blocks of
σ
(n,m)
in the near subcritical phase.
Committee
Boris Pittel (Advisor)
Matthew Kahle (Committee Member)
Saleh Tanveer (Committee Member)
Pages
144 p.
Subject Headings
Mathematics
Keywords
chord diagrams
;
intersection graphs
;
circle graphs
;
permutations
;
permutation graphs
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Acan, H. (2013).
An Enumerative-Probabilistic Study of Chord Diagrams
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1373310487
APA Style (7th edition)
Acan, Huseyin.
An Enumerative-Probabilistic Study of Chord Diagrams.
2013. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1373310487.
MLA Style (8th edition)
Acan, Huseyin. "An Enumerative-Probabilistic Study of Chord Diagrams." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1373310487
Chicago Manual of Style (17th edition)
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Document number:
osu1373310487
Download Count:
1,069
Copyright Info
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.