Van der Waerden's Theorem on Homothetic copies of {1,1+s, 1+s+t}

Every $3$-dimensional convex body can be covered by $14$ smaller homothetic copies

We show that every $3$-dimensional convex body can be covered by $14$ smaller homothetic copies. The previous result was $16$ copies established by Papadoperakis in 1999, while a conjecture by Hadwiger is $8$. We modify Papadoperakis's approach and develop a discretization technique that reduces the problem to verification of feasibility of a number of linear programs with rational coefficients, which is done with computer assistance using exact arithmetic.

广义瓦尔德韦因游戏中的快速获胜策略

Fast winning strategies in a generalized van der Waerden game

研究广义瓦尔德韦因游戏中的获胜策略，证明当$|S|\leq 3$时制胜者可在$|S|$回合内获胜，当$|S|=4$时可在5回合内获胜，而$|S|\geq 5$时无此类策略。