Results 21 to 30 of about 104 (81)
Some Arithmetic Properties of Matroidal Ideals [PDF]
Communications in Algebra, 2010 Let R = K[x 1,…, x n ] denote the polynomial ring in n variables over a field K. A matroidal ideal I is a square-free monomial ideal in R whose minimal generators satisfying the following exchange condition that for any , , if a i > b i for some i, then there exists some j with a j
openaire +1 more source
Robustness Maximization of Parallel Multichannel Systems
Journal of Electrical and Computer Engineering, Volume 2012, Issue 1, 2012., 2012 Bit error rate (BER) minimization and SNR‐gap maximization, two robustness optimization problems, are solved, under average power and bitrate constraints, according to the waterfilling policy. Under peak power constraint the solutions differ and this paper gives bit‐loading solutions of both robustness optimization problems over independent parallel ...
Jean-Yves Baudais +3 more
wiley +1 more source
The Fine-Grained Complexity of Computing the Tutte Polynomial of a Linear Matroid
, 2021 We show that computing the Tutte polynomial of a linear matroid of dimension k on kO(1) points over a field of kO(1) elements requires kΩ(k) time unless the #ETH-a counting extension of the Exponential Time Hypothesis of Impagliazzo and Paturi [CCC 1999]
Andreas Björklund +3 more
core +1 more source
Elliptic arrangements of complex multiplication type
Forum of Mathematics, SigmaWe provide a natural definition of an elliptic arrangement, extending the classical framework to an elliptic curve $\mathcal {E}$ with complex multiplication.
Luca Moci +3 more
doaj +1 more source
The joints problem for matroids [PDF]
, 2018 We prove that in a simple matroid, the maximal number of joints formed by L lines is o(L[superscript 2]) and Ω(L[superscript 2-ε]) for any ε > 0.
Guth, Lawrence, Suk, Andrew
core +1 more source
Connections between Euler Characteristic Invariants, H-Vector Problems, and Algebro-Geometric Properties of (Poly)matroids [PDF]
, 2023 We explore combinatorial questions using tools from algebraic geometry/topology (or the converse). The first direction we start with involves combinatorial constructions approximating and characterizing properties of varieties.
Park, Soohyun
core +1 more source
, 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
Arithmetic Circuits and Neural Networks for Regular Matroids
CoRRWe prove that there exist uniform $(+,\times,/)$-circuits of size $O(n^3)$ to compute the basis generating polynomial of regular matroids on $n$ elements. By tropicalization, this implies that there exist uniform $(\max,+,-)$-circuits and ReLU neural networks of the same size for weighted basis maximization of regular matroids.
Hertrich, Christoph +2 more
openaire +2 more sources
Some arithmetic properties of matroidal ideals
, 2008 In this paper, we study various properties of matroidal ideals.
Chiang-Hsieh, Hung-Jen, Wang, Hsin-Ju
openaire +2 more sources
G-TUTTE多項式の組み合わせ論的、位相的、マトロイド理論的研究
, 2020 We introduce and study the notion of G-Tutte polynomial for a list of elements in a finitely generated abelian group and an abelian group G through combinatorial, topological and matroid theoretical aspects.
TRAN NHAT TAN
core +1 more source