An Alternative Framework for Irreducibility and Primitivity of Nonnegative Tensors

@misc{xu2026alternative,
  title = {{An Alternative Framework for Irreducibility and Primitivity of Nonnegative Tensors}},
  author = {Jianhong Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.30482},
  eprint = {2606.30482},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.30482},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - An Alternative Framework for Irreducibility and Primitivity of Nonnegative Tensors
AU  - Jianhong Xu
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2606.30482
UR  - https://arxiv.org/abs/2606.30482
AB  - Motivated by some recent studies on higher order Markov chains and well-known characterizations for irreducibility and primitivity of nonnegative matrices, we propose in this paper an alternative framework for irreducibility and primitivity of nonnegative tensors, giving rise to two new notions: s-irreducibility and s-primitivity. Our framework includes the relevant results on nonnegative matrices as its special cases, yet it expands existing results regarding irreducibility and primitivity of nonnegative tensors. In addition to its tensor theoretic significance, such a framework has important implications for applied problems such as higher order Markov chains.
ER  -