Combinatorics on minimal transitive factorizations of permutations순열의 호환분해에 관한 조합론

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In this thesis, we give a combinatorial proof for the enumeration of the set ${\mathcal F}_{λ}$ of the minimal transitive factorizations of permutations that have cycle type λ. These factorizations are related to the branched covers of the sphere, which was originally suggested by Hurwitz. In Chapter 2, we introduce some related combinatorial objects - circle chord diagrams, noncrossing partitions, labelled trees, and parking functions. In Chapter 3, we prove that $|{\mathcal F}_{(n)}|=n^{n-2}$, and present an algorithm which generates the elements of ${\mathcal F}_{(n)}$ from parking functions. In Chapter 4, we enumerate some labelled trees combinatorially and count the number of certain parking functions by relating them to labelled trees. In Chapter 5, we give a combinatorial proof of $|{\mathcal F}_{(1,n-1)}|=(n-1)^{n}$ and obtain a refined enumeration of ${\mathcal F}_{(1,n-1)}$ by interpreting them as prime parking functions. In Chapter 6, we construct combinatorial objects whose cardinality is $4(n-1)(n-2)^{n-1}$, and find a bijection from ${\mathcal F}_{(2,n-2)}$ to them.
Advisors
Kim, Dong-Suresearcher김동수researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2004
Identifier
237503/325007  / 000985174
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2004.2, [ v, 43 p. ]

Keywords

COMBINATORICS; BIJECTION; 주차함수; PERMUTATION; TREE; PARKING FUNCTION; 조합론; 일대일대응; 순열; 수형도

URI
http://hdl.handle.net/10203/41870
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=237503&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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