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PreprintarXiv licencearXiv

Linear transformations of tropical matrices preserving individual values of the cyclicity index

  • Alexander Guterman
  • Alexander Vlasov
  • Svetlana Zhilina
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Abstract

The cyclicity index is used to study the periodic behavior of powers of tropical matrices. It is determined by the structure of the critical subgraph of a matrix, which consists of the cycles with the largest average weight. In this paper bijective linear transformations of tropical matrices that preserve an individual value k≠ 2 of this invariant are studied.

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Cite

BibTeXRIS
BibTeX
@misc{guterman2026linear,
  title = {{Linear transformations of tropical matrices preserving individual values of the cyclicity index}},
  author = {Alexander Guterman and Alexander Vlasov and Svetlana Zhilina},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32897},
  eprint = {2610.32897},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32897},
}
RIS
TY  - UNPB
TI  - Linear transformations of tropical matrices preserving individual values of the cyclicity index
AU  - Alexander Guterman
AU  - Alexander Vlasov
AU  - Svetlana Zhilina
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32897
UR  - https://arxiv.org/abs/2610.32897
AB  - The cyclicity index is used to study the periodic behavior of powers of tropical matrices. It is determined by the structure of the critical subgraph of a matrix, which consists of the cycles with the largest average weight. In this paper bijective linear transformations of tropical matrices that preserve an individual value k≠ 2 of this invariant are studied.
ER  -