Displaying similar documents to “When is a 0-1 knapsack a matroid?”

The Tutte polynomial of a morphism of matroids I. Set-pointed matroids and matroid perspectives

Michel Las Vergnas (1999)

Annales de l'institut Fourier

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We study the basic algebraic properties of a 3-variable Tutte polynomial the author has associated with a morphism of matroids, more precisely with a matroid strong map, or matroid perspective in the present paper, or, equivalently by the Factorization Theorem, with a matroid together with a distinguished subset of elements. Most algebraic properties of the usual 2-variable Tutte polynomial of a matroid generalize to the 3-variable polynomial. Among specific properties we show that the...

Broken Circuits in Matroids-Dohmen’s Inductive Proof

Wojciech Kordecki, Anna Łyczkowska-Hanćkowiak (2013)

Discussiones Mathematicae Graph Theory

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Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids

Improvements on the Cantor-Zassenhaus factorization algorithm

Michele Elia, Davide Schipani (2015)

Mathematica Bohemica

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The paper presents a careful analysis of the Cantor-Zassenhaus polynomial factorization algorithm, thus obtaining tight bounds on the performances, and proposing useful improvements. In particular, a new simplified version of this algorithm is described, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but can also provide good estimates and deterministic bounds of the number of operations needed...

Towards the automated synthesis of a Gröbner bases algorithm.

Bruno Buchberger (2004)

RACSAM

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We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates...