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Affine invariant conditions for a class of differential polynomial cubic systems
Acta et Commentationes: Ştiinţe Exacte şi ale NaturiiIn this article the affine invariant criteria constructed in terms of algebraic polynomials with coefficients $\tilde a \in \mathcal R^{20}$ for a class of cubic systems are established.
Cristina Bujac
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Polynomial Invariants for Affine Programs [PDF]
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, 2018 We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given
Hrushovski, Ehud +3 more
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Skew RSK dynamics: Greene invariants, affine crystals and applications toq-Whittaker polynomials
Forum of Mathematics, Pi, 2023 AbstractIterating the skew RSK correspondence discovered by Sagan and Stanley in the late 1980s, we define deterministic dynamics on the space of pairs of skew Young tableaux$(P,Q)$. We find that these skew RSK dynamics display conservation laws which, in the picture of Viennot’s shadow line construction, identify generalizations of Greene invariants ...
Imamura, Takashi +2 more
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A Simple Affine-Invariant Spline Interpolation over Triangular Meshes
Mathematics, 2022 Given a triangular mesh, we obtain an orthogonality-free analogue of the classical local Zlámal–Ženišek spline procedure with simple explicit affine-invariant formulas in terms of the normalized barycentric coordinates of the mesh triangles.
László L. Stachó
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Every locally characterized affine-invariant property is testable [PDF]
, 2013 Let F = F_p for any fixed prime p >= 2. An affine-invariant property is a property of functions on F^n that is closed under taking affine transformations of the domain.
Bhattacharyya, Arnab +4 more
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AN AFFINE INDEX POLYNOMIAL INVARIANT OF VIRTUAL KNOTS [PDF]
Journal of Knot Theory and Its Ramifications, 2013 This paper describes a polynomial invariant of virtual knots that is defined in terms of an integer labeling of the virtual knot diagram. This labeling is seen to derive from an essentially unique structure of affine flat biquandle for flat virtual diagrams.
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Testing Low Complexity Affine-Invariant Properties [PDF]
, 2012 Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties.
Bhattacharyya, Arnab +2 more
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Extended affine Weyl groups and Frobenius manifolds [PDF]
, 1996 We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley theorem for their invariants, and construct a Frobenius structure on their ...
Dubrovin, Boris, Zhang, Youjin
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An Elementary Construction of Modified Hamiltonians and Modified Measures of 2D Kahan Maps [PDF]
Open Communications in Nonlinear Mathematical PhysicsWe show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials defining the ...
Giorgio Gubbiotti +2 more
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Diagonal Coinvariants and Double Affine Hecke Algebras [PDF]
, 2003 We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine Hecke algebra.
Cherednik, Ivan
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