Results 11 to 20 of about 104 (81)
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.
Lenz, Matthias
core +8 more sources
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
D'Adderio M, Moci L
core +8 more sources
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
openaire +4 more sources
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?
Lenz, Matthias
openaire +5 more sources
TheoretiCSWe introduce determinantal sieving, a new, remarkably powerful tool in the toolbox of algebraic FPT algorithms. Given a polynomial $P(X)$ on a set of variables $X=\{x_1,\ldots,x_n\}$ and a linear matroid $M=(X,\mathcal{I})$ of rank $k$, both over a field
Eduard Eiben +2 more
doaj +3 more sources
Unmixedness and arithmetic properties of matroidal ideals [PDF]
Archiv der Mathematik, 2019 AbstractLet $$R=k[x_1,\ldots ,x_n]$$R=k[x1,…,xn] be the polynomial ring in n variables over a field k and let I be a matroidal ideal of degree d. In this paper, we study the unmixedness properties and the arithmetical rank of I. Moreover, we show that $$ara(I)=n-d+1$$ara(I)=n-d+1.
Hero Saremi, Amir Mafi
openaire +3 more sources
Erratum: Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements (Trans. Amer. Math. Soc. (2020) 373:3 (1909-1940) DOI: 10.1090/tran/7952) [PDF]
, 2020 In this short note we correct the statement of the main result of [Trans. Amer. Math. Soc. 373 (2020), no. 3, 1909-1940]. That paper presented the rational cohomology ring of a toric arrangement by generators and relations. One of the series of relations
Delucchi, Emanuele +4 more
core +2 more sources
Parameterized Applications of Symbolic Differentiation of (Totally) Multilinear Polynomials [PDF]
, 2021 We study the following problem and its applications: given a homogeneous degree-d polynomial g as an arithmetic circuit C, and a d × d matrix X whose entries are homogeneous linear polynomials, compute g(∂/∂ x₁, …, ∂/∂ x_n) det X.
Pratt, Kevin, Brand, Cornelius
core +1 more source
Towards Nearly-Linear Time Algorithms for Submodular Maximization with a Matroid Constraint [PDF]
, 2019 We consider fast algorithms for monotone submodular maximization subject to a matroid constraint. We assume that the matroid is given as input in an explicit form, and the goal is to obtain the best possible running times for important matroids.
Nguyen, Huy L., Ene, Alina
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Definable sets up to definable bijections in Presburger groups
Transactions of the London Mathematical Society, Volume 5, Issue 1, Page 47-70, December 2018., 2018 Abstract We entirely classify definable sets up to definable bijections in Z‐groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable sets.
Raf Cluckers, Immanuel Halupczok
wiley +1 more source