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PreprintCC BY 4.0arXiv

Dense alternating sign matrices and imprecise copulas

  • Tomaž Košir
  • Elisa Perrone
  • Nik Stopar
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Abstract

In this paper, we study discrete quasi-copulas and discrete imprecise copulas of minimal range, which naturally correspond to alternating sign matrices. We identify dense alternating sign matrices as a particularly well-behaved subclass. We prove that the associated discrete imprecise copulas are always coherent and hence avoid sure loss. We further show that a particular extension of the corresponding discrete quasi-copulas to the full domain preserves this structure and yields self-dual imprecise copulas. To the best of our knowledge, this provides the first general result in the literature showing how properties established for discrete imprecise copulas can be preserved when extending them to their full-domain counterpart. We conclude the paper by showing that, for general alternating sign matrices, the associated discrete imprecise copulas need not avoid sure loss, further emphasizing the special role of the subclass of dense alternating sign matrices. We establish, however, that the class of discrete quasi-copulas of minimal range is invariant under all defect transformations

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Cite

BibTeXRIS
BibTeX
@misc{kosir2026dense,
  title = {{Dense alternating sign matrices and imprecise copulas}},
  author = {Tomaž Košir and Elisa Perrone and Nik Stopar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.06178},
  eprint = {2607.06178},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.06178},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Dense alternating sign matrices and imprecise copulas
AU  - Tomaž Košir
AU  - Elisa Perrone
AU  - Nik Stopar
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2607.06178
UR  - https://arxiv.org/abs/2607.06178
AB  - In this paper, we study discrete quasi-copulas and discrete imprecise copulas of minimal range, which naturally correspond to alternating sign matrices. We identify dense alternating sign matrices as a particularly well-behaved subclass. We prove that the associated discrete imprecise copulas are always coherent and hence avoid sure loss. We further show that a particular extension of the corresponding discrete quasi-copulas to the full domain preserves this structure and yields self-dual imprecise copulas. To the best of our knowledge, this provides the first general result in the literature showing how properties established for discrete imprecise copulas can be preserved when extending them to their full-domain counterpart. We conclude the paper by showing that, for general alternating sign matrices, the associated discrete imprecise copulas need not avoid sure loss, further emphasizing the special role of the subclass of dense alternating sign matrices. We establish, however, that the class of discrete quasi-copulas of minimal range is invariant under all defect transformations
ER  -