A1 Refereed original research article in a scientific journal
On injective multivariate polynomials over rational numbers; 
Authors: Hirvensalo, Mika
Publisher: Elsevier BV
Publication year: 2026
Journal: Theoretical Computer Science
Article number: 116158
Volume: 1082
ISSN: 0304-3975
eISSN: 1879-2294
DOI: https://doi.org/10.1016/j.tcs.2026.116158
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1016/j.tcs.2026.116158
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/526990307
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
Let ℙ be the set of prime numbers. We show that for each finite set Π ⊆ ℙ ⧵ {2}, there exists a subring ΛΠ ⊆ ℚ and an injective polynomial function 𝑃∶ ΛΠ × ΛΠ → ΛΠ.
Keywords:
injective functions, multivariate polynomials, Probabilistic automata
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