Complete classification of 3-multisets up to combinatorial equivalence
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- 作者：Davi Lopes Alves de Medeiros1 ; davi_lopes90@hotmail.com ; Lev Birbrair ; 2 ; birb@ufc.br
- 关键词：11B30 ; 05A17
- 刊名：Journal of Number Theory
- 出版年：2017
- 出版时间：May 2017
- 年：2017
- 卷：174
- 期：Complete
- 页码：68-77
- 全文大小：273 K
- 卷排序：174
文摘
Let A={a1,…,ak}A={a1,…,ak} be a finite multiset of positive real numbers. Consider the sequence of all positive integers multiples of all aiai's, and note the multiplicity of each term in this sequence. This sequence of multiplicities is called the resonance sequence generated by {a1,…,ak}{a1,…,ak}. Two multisets are called combinatorially equivalent if they generate the same resonance sequence. The paper gives a complete criterion of classification of multisets with 3 elements up to combinatorial equivalence, by showing this is equivalent to a system of equations depending directly of the numbers in the multisets.VideoFor a video summary of this paper, please visit https://youtu.be/rf12nhySOJQ.