Results 21 to 30 of about 99,592 (142)
Coalgebraic Satisfiability Checking for Arithmetic $\mu$-Calculi [PDF]
Logical Methods in Computer ScienceThe coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based.
Daniel Hausmann, Lutz Schröder
doaj +1 more source
A construction of integer-valued polynomials with prescribed sets of lengths of factorizations [PDF]
, 2013 For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n ...
Ch Frei +4 more
core +2 more sources
Multiplicative polynomials and Fermat's little theorem for non-primes
International Journal of Mathematics and Mathematical Sciences, 1997 Fermat's Little Theorem states that xp=x(modp) for x∈N and prime p, and so identifies an integer-valued polynomial (IVP) gp(x)=(xp−x)/p. Presented here are IVP's gn for non-prime n that complete the sequence {gn|n∈N} in a natural way.
Paul Milnes, C. Stanley-Albarda
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Polynomial extension of Fleck's congruence [PDF]
, 2005 Let $p$ be a prime, and let $f(x)$ be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the $p$-adic order of the sum $$\sum_{k=r(mod p^{\beta})}\binom{n}{k}(-1)^k f([(k-r)/p^{\alpha}]),$$ where $\alpha\ge ...
Sun, Zhi-Wei
core +3 more sources
Discrete Analysis, 2020 An algebraic inverse theorem for the quadratic Littlewood-Offord problem, and an application to Ramsey graphs, Discrete Analysis 2020:12, 34 pp. The Littlewood-Offord problem is the following general question.
Matthew Kwan, Lisa Sauermann
doaj +1 more source
Integer-Valued Polynomials on a Subset [PDF]
Proceedings of the American Mathematical Society, 1993 Let \(D\) be an integral domain, which is not a field, \(K\) its quotient field, \(D'\) the integral closure of \(D\) and \(\emptyset\subsetneqq E\subseteqq K\). Let \(\text{Int}(E,D)=\bigl\{f\in K[X];f(E)\subseteqq D\bigr\}\) be the ring of integer-valued polynomials.
openaire +1 more source
Integer-valued polynomials over matrices and divided differences
, 2013 Let $D$ be an integrally closed domain with quotient field $K$ and $n$ a positive integer. We give a characterization of the polynomials in $K[X]$ which are integer-valued over the set of matrices $M_n(D)$ in terms of their divided differences.
Peruginelli, Giulio
core +3 more sources
Polynomial overrings of ${\rm Int}(\mathbb Z)$
, 2016 We show that every polynomial overring of the ring ${\rm Int}(\mathbb Z)$ of polynomials which are integer-valued over $\mathbb Z$ may be considered as the ring of polynomials which are integer-valued over some subset of $\hat{\mathbb{Z}}$, the profinite
Chabert, Jean-Luc, Peruginelli, Giulio
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Detecting integral polyhedral functions [PDF]
, 2008 We study the class of real-valued functions on convex subsets of R^n which are computed by the maximum of finitely many affine functionals with integer slopes.
Kedlaya, Kiran S., Tynan, Philip
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The ring of polynomials integral-valued over a finite set of integral elements [PDF]
, 2016 Let $D$ be an integral domain with quotient field $K$ and $\Omega$ a finite subset of $D$. McQuillan proved that the ring ${\rm Int}(\Omega,D)$ of polynomials in $K[X]$ which are integer-valued over $\Omega$, that is, $f\in K[X]$ such that $f(\Omega ...
Peruginelli, G.
core +2 more sources