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PreprintCC BY 4.0arXiv

Finite algebras whose equational probability spectrum contains a big gap

  • Carles Cardó
  • Keith A. Kearnes
  • Ágnes Szendrei
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Abstract

We classify the finite algebras A for which there is no value p satisfying 1/|A|<p<1 in the equational probability spectrum of A. We will use the classification to determine which finite algebras have minimal equational probability spectrum. In our final section, we explore the relationship, for finite algebras, between the properties of (i)~having a finite equational probability spectrum and (ii)~being an abelian algebra.

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Cite

BibTeXRIS
BibTeX
@misc{cardo2026finite,
  title = {{Finite algebras whose equational probability spectrum contains a big gap}},
  author = {Carles Cardó and Keith A. Kearnes and Ágnes Szendrei},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37841},
  eprint = {2610.37841},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37841},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Finite algebras whose equational probability spectrum contains a big gap
AU  - Carles Cardó
AU  - Keith A. Kearnes
AU  - Ágnes Szendrei
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37841
UR  - https://arxiv.org/abs/2610.37841
AB  - We classify the finite algebras A for which there is no value p satisfying 1/|A|<p<1 in the equational probability spectrum of A. We will use the classification to determine which finite algebras have minimal equational probability spectrum. In our final section, we explore the relationship, for finite algebras, between the properties of (i)~having a finite equational probability spectrum and (ii)~being an abelian algebra.
ER  -