Results 11 to 20 of about 102 (70)
Discrete Mathematics & Theoretical Computer Science, 2013 We introduce the notion of a matroid $M$ over a commutative ring $R$, assigning to every subset of the ground set an $R$-module according to some axioms. When $R$ is a field, we recover matroids.
Alex Fink, Luca Moci
doaj +3 more sources
The Arithmetic Tutte polynomial of two matrices associated to Trees
Special Matrices, 2018 Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors
Bapat R. B. +1 more
doaj +2 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
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Arithmetic matroids, Tutte polynomial, and toric arrangements
, 2011 We introduce the notion of an arithmetic matroid, whose main example is given by 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.
D'Adderio, Michele, Moci, Luca
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Rectilinear approximation and volume estimates for hereditary bodies via [0, 1]‐decorated containers
Journal of Graph Theory, Volume 104, Issue 1, Page 104-132, September 2023., 2023 Abstract We use the hypergraph container theory of Balogh–Morris–Samotij and Saxton–Thomason to obtain general rectilinear approximations and volume estimates for sequences of bodies closed under certain families of projections. We give a number of applications of our results, including a multicolour generalisation of a theorem of Hatami, Janson and ...
Victor Falgas‐Ravry +3 more
wiley +1 more source
On generalisations of the Aharoni–Pouzet base exchange theorem
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1540-1549, June 2023., 2023 Abstract The Greene–Magnanti theorem states that if M$ M$ is a finite matroid, B0$ B_0$ and B1$ B_1$ are bases and B0=⋃i=1nXi$ B_0=\bigcup _{i=1}^{n} X_i$ is a partition, then there is a partition B1=⋃i=1nYi$ B_1=\bigcup _{i=1}^{n}Y_i$ such that (B0∖Xi)∪Yi$ (B_0 \setminus X_i) \cup Y_i$ is a base for every i$ i$. The special case where each Xi$ X_i$ is
Zsuzsanna Jankó, Attila Joó
wiley +1 more source
On the cohomology of arrangements of subtori
Journal of the London Mathematical Society, Volume 106, Issue 3, Page 1999-2029, October 2022., 2022 Abstract Given an arrangement of subtori of arbitrary codimension in a complex torus, we compute the cohomology groups of the complement. Then, by using the Leray spectral sequence, we describe the multiplicative structure on the associated graded cohomology. We also provide a differential model for the cohomology ring, by considering a toric wonderful
Luca Moci, Roberto Pagaria
wiley +1 more source
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
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, 2015 We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids.
Luca Moci +7 more
core +1 more source
G-Tutte Polynomials and Abelian Lie Group Arrangements [PDF]
, 2021 For a list A of elements in a finitely generated abelian group Gamma and an abelian group G, we introduce and study an associated G-Tutte polynomial, defined by counting the number of homomorphisms from associated finite abelian groups to G.
Tan Nhat Tran +2 more
core +1 more source