🤖 AI Summary
研究通过图的自同构群分析匹配模型中的马尔可夫链强聚合性，扩展了贪婪和非贪婪匹配规则下的强聚合条件。
📝 Abstract
We extend the analysis of strong aggregation to general compatibility graphs, focusing on item counts rather than positions, and exploring generalized greedy matching disciplines. We prove that under a condition of automorphism-based transition consistency, the associated Markov chain is strongly aggregable for an arbitrary graph with a non-trivial automorphism group. Furthermore, we extend our analysis to non-greedy matching disciplines, distinguishing scenarios where compatible items can or cannot coexist within the same state. This result is illustrated with a simple compatibility graph with a rich automorphism structure: the odd rings. For all scenarios, we investigate the strong aggregation properties of the resulting Markov chains. This work enhances the theoretical understanding of lumpability in stochastic matching models and provides a foundation for analyzing complex graph structures.