Young's lattice and rank functions of differential posetsYoung의 격자와 Differential Poset의 순위함수

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We discuss some conjectures for rank functions of differential posets, and show that these conjectures hold for the Young`s lattice and its Cartesian products. Miller and Stanley conjectured that any differential poset has the nondecreasing property of 1st difference and the nonnegative property of $t$-th difference. Moreover, the inequality ${p_{n + 1}} \le r{p_n} + {p_{n - 1}}$ is the other conjecture raised by Stanley, where $p_n$ is the number of elements in an $r$-differential poset of rank $n$. In this thesis, we show that this inequality establishs for the Young`s lattice and its Cartesian products by constructing injections.
Advisors
Kwak, Si-Jongresearcher곽시종
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2013
Identifier
515077/325007  / 020113662
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수리과학과, 2013.2, [ iv, 24 p. ]

Keywords

Young`s lattice; differential poset; Young의 격자; differential poset; 순위함수; rank function

URI
http://hdl.handle.net/10203/181566
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=515077&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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