조수진
길도영
2019-08-13T16:40:38Z
2019-08-13T16:40:38Z
2019-08
29082
https://dspace.ajou.ac.kr/handle/2018.oak/15425
학위논문(석사)--아주대학교 일반대학원 :수학과,2019. 8
In this thesis, we introduce a problem in number theory posed by Erdős and Moser in 1965, and a solution provided by Stanley who used a technique in algebraic geometry.
Erdős–Moser Problem is about the sum of subsets of finite set. More precisely, let S⊂R be a finite set. For any α∈R, define f(S,α)=|{T⊂S : Σ_{t∈T}{t}=α}|. Erdős–Moser Problem asks how large f(S,α) can be if we require |S|=n. Erdős–Moser Conjecture that was introduced in 1965, asserts that if |S|=2m+1, then f(S,α)≤ f({-m,-m+1,...,m},0). Stanley proved the conjecture in1980: Let S be a set of 2l+1 distinct real numbers and let T_{1},...,T_{k} be subsets of S whose element sums are equal. Then k does not exceed the middle coefficient of the polynomial 2(1+q)²(1+q²)²…(1+q^{l})², and this bound is best possible. We study Stanley's results including variations of Erdős–Moser Problems. Then we consider another variation of Erdős–Moser Problem by restricting the number of elements and give a solution to the problem by applying Stanley's result.
1. Introduction 1
2. Premliminaries 3
3. Stanley's Result 6
3.1. Type A_n 6
3.2. Type B_n 10
3.3 Stanley's Reusults on On Erdős–Moser Problems 12
4. A variation of Erdős–Moser Problems 16
eng
The Graduate School, Ajou University
아주대학교 논문은 저작권에 의해 보호받습니다.
On Erdős–Moser Problems
Thesis
아주대학교 일반대학원
일반대학원 수학과
2019. 8
Master
952045
I804:41038-000000029082
http://dcoll.ajou.ac.kr:9080/dcollection/common/orgView/000000029082