88304am永利集团

Amdeberhan's conjectures concerning the enumeration, average size, and largest size of strict $(n,n+1)$-core partitions have stimulated extensive research in this area. Nevertheless, the investigation of random core partitions remains relatively underdeveloped. In this talk, we first present several polynomiality results and asymptotic formulas for the moments of sizes of random strict $(n, dn\pm 1)$-core partitions. We further establish the asymptotic normality of their sizes. Analogous results are also derived for random (strict) $n$-core partitions and random self-conjugate $n$-core partitions with bounded perimeters. These findings resolve several conjectures posed by Zaleski and stand in contrast to the asymptotic behavior derived by Even-Zohar in 2022 for the size of a random $(s,t)$-core partition with coprime $s$ and $t$, which converges in distribution to Watson’s $U^2$ distribution. These are joint works with Wenston J.T. Zang, Yetong Sha, and Jiange Li.

熊欢，哈尔滨工业大学数学研究院教授/科研副院长。研究方向为代数组合和机器学习。在TPAMI, JMLR, JCTA, Sci. China Math., ICML, NBER等国际知名期刊和会议发表论文50余篇，被引用次数2000多次。主持或参与瑞士国家自然科学基金、法国国家科研中心的多项研究项目。入选2024年“小米青年学者”。自2024年起担任中国工业与应用数学学会图论组合及应用专委会委员。担任人工智能国际顶级会议ICLR 2026领域主席。