Results 1 to 10 of about 56 (47)
Splines, lattice points, and (arithmetic) matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Let $X$ be a $(d \times N)$-matrix. We consider the variable polytope $\Pi_X(u) = \left\{ w \geq 0 : Xw = u \right\}$. It is known that the function $T_X$ that assigns to a parameter $u \in \mathbb{R}^N$ the volume of the polytope $\Pi_X(u)$ is piecewise
Matthias Lenz
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Arithmetic matroids and Tutte polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce the notion of arithmetic matroid, whose main example is provided by a list of elements in a finitely generated abelian group. We study the representability of its dual, and, guided by the geometry of toric arrangements, we give a ...
Michele D'Adderio, Luca Moci
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Representations of torsion-free arithmetic matroids [PDF]
European Journal of Combinatorics, 2021 We study the representability problem for torsion-free arithmetic matroids. By using a new operation called "reduction" and a "signed Hermite normal form", we provide and implement an algorithm to compute all the representations, up to equivalence. As an application, we disprove two conjectures about the poset of layers and the independence poset of a ...
Roberto Pagaria, Giovanni Paolini
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Orientable arithmetic matroids [PDF]
Discrete Mathematics, 2020 13 pages, 1 ...
Roberto Pagaria
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On powers of Plücker coordinates and representability of arithmetic matroids [PDF]
Advances in Applied Mathematics, 2020 The first problem we investigate is the following: given $k\in \mathbb{R}_{\ge 0}$ and a vector $v$ of Plücker coordinates of a point in the real Grassmannian, is the vector obtained by taking the $k$th power of each entry of $v$ again a vector of Plücker coordinates?
Matthias Lenz
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The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids [PDF]
Journal of Algebra, 2021 Final version, to appear on Journal of ...
Winfried Bruns +2 more
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Representations of Weakly Multiplicative Arithmetic Matroids are Unique [PDF]
Annals of Combinatorics, 2019 An arithmetic matroid is weakly multiplicative if the multiplicity of at least one of its bases is equal to the product of the multiplicities of its elements. We show that if such an arithmetic matroid can be represented by an integer matrix, then this matrix is uniquely determined.
Matthias Lenz
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Products of arithmetic matroids and quasipolynomial invariants of CW-complexes [PDF]
Journal of Combinatorial Theory - Series A, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Emanuele Delucchi, Luca Moci
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Arithmetic matroids, the Tutte polynomial and toric arrangements [PDF]
Advances in Mathematics, 2013 AbstractWe introduce the notion of an arithmetic matroid whose main example is a list of elements of a finitely generated abelian group. In particular, we study the representability of its dual, providing an extension of the Gale duality to this setting. Guided by the geometry of generalized toric arrangements, we provide a combinatorial interpretation
Luca Moci
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The multivariate arithmetic Tutte polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two.
Petter Brändèn, Luca Moci
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