Some results on Archdeacon's conjecture for rotation systems
本文通过计算验证Archdeacon关于旋转系统中非平面四元素子集数量的猜想，并证明了对于n个元素的旋转系统，至少存在(8/9-o(1))H(n)个非平面四元素子集。
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A note on markets with semi-static trading strategies
研究了半静态交易策略下的金融市场套利问题，通过引入随机变量小锥概念，并提供其在概率意义下闭合的充分条件。
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From the Social Choice Problem to a Collusion-Proof Tendering Mechanism for Dynamic Stochastic Projects
本文针对动态随机项目中的社会选择问题，提出了一种防共谋的投标机制TU-GUM，改进了AGV机制的不足，并适用于更广泛的动态环境。
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Countable Graphs with Finite Path-width: Characterisation and Universality
研究了可数无限图的路径宽度和线宽，通过特定条件刻画有限路径宽度的图，并探讨了具有有界路径或线宽图的普遍性问题。
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Weighted Equitability and Matroid-Constrained Discrepancy
This study addresses weighted fair division and discrepancy theory under matroid constraints, proposing strongly polynomial-time algorithms grounded in local exchange theorems and constructive proofs. Key contributions include establishing weighted matroid partitionability and extending the Beck-Fiala framework to matroid settings, yielding logarithmic discrepancy bounds. The work achieves EF1 and additive approximation guarantees for fair allocation and scheduling optimization while refuting the weighted carpool conjecture. By systematically resolving fairness and discrepancy control challenges in constrained environments, this research provides novel theoretical foundations and efficient algorithmic tools for related combinatorial optimization problems.
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Some results on Archdeacon's conjecture for rotation systems
本文通过计算验证Archdeacon关于旋转系统中非平面四元素子集数量的猜想，并证明了对于n个元素的旋转系统，至少存在(8/9-o(1))H(n)个非平面四元素子集。
0 citationsRead paper
A note on markets with semi-static trading strategies
研究了半静态交易策略下的金融市场套利问题，通过引入随机变量小锥概念，并提供其在概率意义下闭合的充分条件。
0 citationsRead paper
From the Social Choice Problem to a Collusion-Proof Tendering Mechanism for Dynamic Stochastic Projects
本文针对动态随机项目中的社会选择问题，提出了一种防共谋的投标机制TU-GUM，改进了AGV机制的不足，并适用于更广泛的动态环境。
0 citationsRead paper
Countable Graphs with Finite Path-width: Characterisation and Universality
研究了可数无限图的路径宽度和线宽，通过特定条件刻画有限路径宽度的图，并探讨了具有有界路径或线宽图的普遍性问题。
0 citationsRead paper
Weighted Equitability and Matroid-Constrained Discrepancy
This study addresses weighted fair division and discrepancy theory under matroid constraints, proposing strongly polynomial-time algorithms grounded in local exchange theorems and constructive proofs. Key contributions include establishing weighted matroid partitionability and extending the Beck-Fiala framework to matroid settings, yielding logarithmic discrepancy bounds. The work achieves EF1 and additive approximation guarantees for fair allocation and scheduling optimization while refuting the weighted carpool conjecture. By systematically resolving fairness and discrepancy control challenges in constrained environments, this research provides novel theoretical foundations and efficient algorithmic tools for related combinatorial optimization problems.
0 citationsRead paper