Estimates the size of polynomial orbits under transitive actions in discrete valuation domains, indicating broader implications for algebraic structures.
Let [Formula: see text] be a discrete valuation domain. In this paper we give an estimation for the number of elements of a set [Formula: see text], on which there acts a family of polynomial mappings in a transitive way. This estimation then applies to orbits in [Formula: see text]. Orbits in [Formula: see text] are examined more closely.
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T. Pezda (2026) studied this question.
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