Euler's Partition Theorem with Upper Bounds on Multiplicities

Electronic Journal Of Combinatorics

William Y.C. Chen¹ 

关键词: partition;    Euler';    s partition theorem;    Sylvester';    s bijection;   

DOI  :  

学科分类：离散数学和组合数学

来源: Electronic Journal Of Combinatorics

【 摘 要 】

We show that the number of partitions of $n$ with alternating sum $k$ such that the multiplicity of each part is bounded by $2m+1$ equals the number of partitions of $n$ with $k$ odd parts such that the multiplicity of each even part is bounded by $m$. Th

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