van der Waerden數(shù)與Ramsey數(shù)問題的研究.pdf

1、上海大學(xué)碩士學(xué)位論文vanderWaerden數(shù)與Ramsey數(shù)問題的研究姓名：胡妍申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：黃益如20050401AbstractIIThismasterthesisfocusesoilvanderWaerdenNumberandRamseyNumberinCombinationMathematicsTheresearchaimsandmainpointsaretheupperboundsofth

2、egeneralizedvanderWaerdennumbersltheupperboundsofvanderWaerdennumbersoncircle，andthenewupperboundformulasofRamseynumbersFirstly，weintroducethedevelopmentsurveyaudmainresearchdirectionsofvanderWaerdenproblemandRamseyTheor

3、yandtheauthor’sresearchworksTheresearchworksofthisthesisconsmtsoftwopartsThefirstaspectoftheresearchworkisstudythegeneralizedvanderWaerdennumbersandvD21derWaerdennumbersoncircleWecomparevanderWaerdennumbersoncircleWh(n，憶

4、)withclassicalvailderWaerdennuulbersw(n，n)byfoundingseveraltheoremsWeaskforWa(n1n)tomakesomeimprovementfortheupperboundsofw(n，n)wecalculatesomeupperhoundsofthegeneralizedvailderWaerdennumbersandvanderWaerdennumbersOllckd

5、ebycomputer，andgetsomeresultsWetrytoavoiddrawerprinciple，buildtheⅡwmethods，generalisevanderWaerdennumbers，andtransformvailderWaerdenproblemintothesolutionsoflinearinequalitiesequationsWehavebuiltthelinearinequalitiesequa

6、tions，andpointoutthatitssolutionscarlbeaskedTheotherpartoftheresearchworkisthatwegetanewupper—lowerboundformulasforRamseynumberswithparametersandaseriesofbetterresults，byusingthenewupperboundformulas，onthefoundationofthe