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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2507.17890 |
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| _version_ | 1866908463799468032 |
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| author | Borovik, Viktoriia Flavi, Cosimo Pielasa, Paweł Shatsila, Anatoli Song, Jeyoung |
| author_facet | Borovik, Viktoriia Flavi, Cosimo Pielasa, Paweł Shatsila, Anatoli Song, Jeyoung |
| contents | The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individual ranks. In the last decades, this conjecture has been a central topic in tensor rank theory and its implications for computational complexity. In 2019, Yaroslav Shitov disproved this conjecture in its general form by showing the existence of a counter-example using a dimension counting argument. In this paper, we provide an overview of the Strassen problem and Shitov's work and revisit his counterexample with a detailed explanation, offering an alternative proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the construction of a counterexample to Strassen's rank additivity conjecture Borovik, Viktoriia Flavi, Cosimo Pielasa, Paweł Shatsila, Anatoli Song, Jeyoung Algebraic Geometry The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individual ranks. In the last decades, this conjecture has been a central topic in tensor rank theory and its implications for computational complexity. In 2019, Yaroslav Shitov disproved this conjecture in its general form by showing the existence of a counter-example using a dimension counting argument. In this paper, we provide an overview of the Strassen problem and Shitov's work and revisit his counterexample with a detailed explanation, offering an alternative proof. |
| title | On the construction of a counterexample to Strassen's rank additivity conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.17890 |