Results 21 to 30 of about 102 (70)
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
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
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
Matroids : h-vectors, zonotopes, and Lawrence polytopes [PDF]
, 2015 The main objects of study in this thesis are matroids. In particular we are interested in three particular classes matroids: regular matroids, arithmetic matroids, and internally perfect matroids.
Dall, Aaron Matthew
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
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
Universal Tutte characters via combinatorial coalgebras [PDF]
, 2018 The Tutte polynomial is the most general invariant of matroids and graphs that can be computed recursively by deleting and contracting edges. We generalize this invariant to any class of combinatorial objects with deletion and contraction operations ...
Moci L, Dupont C, Fink A
core +3 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
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