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PreprintCC BY 4.0arXiv

Enumeration of certain permutation group polynomials

  • Sartaj Ul Hasan
  • Ramandeep Kaur
  • Hridesh Kumar
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Abstract

We construct a new family of permutation group polynomials over finite fields of odd characteristic and explicitly provide its companion. Moreover, we precisely determine the number of permutation group polynomials of this form and those that are equivalent to this new family. In addition, we completely solve the problem of enumerating permutation group polynomials of the various forms presented in Hasan and Kumar (2026), as well as permutation group polynomials which are equivalent to these families.

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Cite

BibTeXRIS
BibTeX
@misc{hasan2026enumeration,
  title = {{Enumeration of certain permutation group polynomials}},
  author = {Sartaj Ul Hasan and Ramandeep Kaur and Hridesh Kumar},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28118},
  eprint = {2608.28118},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28118},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Enumeration of certain permutation group polynomials
AU  - Sartaj Ul Hasan
AU  - Ramandeep Kaur
AU  - Hridesh Kumar
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28118
UR  - https://arxiv.org/abs/2608.28118
AB  - We construct a new family of permutation group polynomials over finite fields of odd characteristic and explicitly provide its companion. Moreover, we precisely determine the number of permutation group polynomials of this form and those that are equivalent to this new family. In addition, we completely solve the problem of enumerating permutation group polynomials of the various forms presented in Hasan and Kumar (2026), as well as permutation group polynomials which are equivalent to these families.
ER  -