Integer-valued functions defined locally by integer polynomials

Paper Title:

Locally Integer Polynomial Functions

Published on:

31 January 2024

Primary Category:

Number Theory

Paper Authors:

Alexander Borisov

Bullets

Key Details

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Functions studied have integer polynomial restrictions to finite integer sets

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Such functions form a commutative ring containing integer polynomials

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They are characterized by integer sequences and bijections of naturals

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The ring contains units -1 and 1 and is closed under composition

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Bounds relate growth rate of these functions to degree of polynomials

Explore the topics in this paper

commutative rings

composition

derivatives

integer-valued functions

polynomials

AI generated summary

Integer-valued functions defined locally by integer polynomials

This paper introduces an interesting class of integer-valued functions on the integers. These functions have the property that their restriction to any finite subset of the integers is given by a polynomial with integer coefficients. The paper studies properties of this class of functions, which form a commutative ring containing the integer polynomials. Key results characterize these functions, show they are closed under composition and discrete derivatives, and investigate bounds on their growth rates.