
Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
In this paper we study systems of autonomous algebraic ODEs in several d...
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Bounds for elimination of unknowns in systems of differentialalgebraic equations
Elimination of unknowns in systems of equations, starting with Gaussian ...
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Fast Computation of the Nth Term of an Algebraic Series over a Finite Prime Field
We address the question of computing one selected term of an algebraic p...
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Notes on Computational Graph and Jacobian Accumulation
The optimal calculation order of a computational graph can be represente...
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Stream/block ciphers, difference equations and algebraic attacks
In this paper we model a class of stream and block ciphers as systems of...
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On Differentially Algebraic Generating Series for Walks in the Quarter Plane
We refine necessary and sufficient conditions for the generating series ...
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Alignment Elimination from Adams' Grammars
Adams' extension of parsing expression grammars enables specifying inden...
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Wilf classes of nonsymmetric operads
Two operads are said to belong to the same Wilf class if they have the same generating series. We discuss possible Wilf classifications of nonsymmetric operads with monomial relations. As a corollary, this would give the same classification for the operads with a finite Groebner basis. Generally, there is no algorithm to decide whether two finitely presented operads belong to the same Wilf class. Still, we show that if an operad has a finite Groebner basis, then the monomial basis of the operad forms an unambiguous contextfree language. Moreover, we discuss the deterministic grammar which defines the language. The generating series of the operad can be obtained as a result of an algorithmic elimination of variables from the algebraic system of equations defined by the Chomsky–Schutzenberger enumeration theorem. We then focus on the case of binary operads with a single relation. The approach is based on the results by Rowland on pattern avoidance in binary trees. We improve and refine Rowland's calculations and empirically confirm his conjecture. Here we use both the algebraic elimination and the direct calculation of formal power series from algebraic systems of equations. Finally, we discuss the connection of Wilf classes with algorithms for the Quillen homology of operads calculation.
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