Complete classification of 3-multisets up to combinatorial equivalence
| Autor: | Davi Lopes Alves de Medeiros, Lev Birbrair |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Multiset Algebra and Number Theory 010102 general mathematics Multiplicity (mathematics) 0102 computer and information sciences System of linear equations 01 natural sciences Combinatorics 010201 computation theory & mathematics 0101 mathematics Equivalence (formal languages) Positive real numbers Multiple Mathematics |
| Zdroj: | Journal of Number Theory. 174:68-77 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2016.09.035 |
| Popis: | Text Let A = { a 1 , … , a k } be a finite multiset of positive real numbers. Consider the sequence of all positive integers multiples of all a i 's, and note the multiplicity of each term in this sequence. This sequence of multiplicities is called the resonance sequence generated by { a 1 , … , a k } . 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. Video For a video summary of this paper, please visit https://youtu.be/rf12nhySOJQ . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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