关于Han型与Shearer型信息不等式：等号条件及组合应用
On Han- and Shearer-Type Information Inequalities: Equality Conditions and Combinatorial Applications
AI总结：
本研究推导强分数不等式间隙分解式，确定Han不等式等号条件，刻画相关投影不等式等号条件，将弱分数不等式应用于极值图论并扩展已有结果。
摘要：
Madiman和Tetali建立了强、弱分数不等式，涵盖Han不等式和Shearer引理等经典熵子集不等式。本研究推导了强分数不等式间隙的分解式，并用其确定强形式Han不等式等号成立的充要条件；据此刻画了Balister与Bollobás（2012）提出的强Loomis-Whitnet型投影不等式的等号条件；最后将弱分数不等式应用于极值图论问题，复现并扩展了Sason（2022）及Boucheron等人（2013）的结果，后者的方法依赖Han不等式。
英文摘要：
Madiman and Tetali established strong and weak fractional inequalities that subsume classical entropy subset inequalities such as Han's inequality and Shearer's lemma. In this work, we derive a decomposition of the gap in the strong fractional inequality and use it to establish the necessary and sufficient conditions for equality in the strong form of Han's inequality. As a consequence, we characterize the equality conditions for a strong Loomis-Whitnet-type projection inequality of Balister and Bollobas (2012). Finally, we apply the weak fractional inequality to an extremal graph theory problem, recovering and extending results of Sason (2022) and Boucheron et al. (2013), whose approaches rely on Han's inequality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
