Related papers: Classification of Minimal Polygons with Specified …

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

We describe the ordering of a class of clones by minion homomorphisms, also known as minor preserving maps or height 1 clone homomorphisms. The class consists of all clones on finite sets determined by binary relations whose projections to…

The main requisite for fine-grained recognition task is to focus on subtle discriminative details that make the subordinate classes different from each other. We note that existing methods implicitly address this requirement and leave it to…

We introduce a class of Laurent polynomials, called maximally mutable Laurent polynomials (MMLPs), that we believe correspond under mirror symmetry to Fano varieties. A subclass of these, called rigid, are expected to correspond to Fano…

This article proposes an algorithm that constructs a Sullivan minimal model for any simply connected simplicial set with effective homology and thereby allows one to decide algorithmically whether two simply connected spaces represented by…

We show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of a recent algorithm of A. Salagean.

We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.

All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…

We consider a class of finite Markov moment problems with arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the non-unique solution families.…

In order to classify concordance classes of codimension 2 embeddings in a manifold M, we need to determine the complement of such an embedding. These complements are spaces over M well defined up to some homology equivalence. We construct a…

We prove a quantitative estimate on the number of certain singularities in almost minimizing clusters. In particular, we consider the singular points belonging to the lowest stratum of the Federer-Almgren stratification (namely, where each…

We algorithmically compute integral Eilenberg-MacLane homology of all semigroups of order at most $8$ and present some particular semigroups with notable classifying spaces, refuting conjectures of Nico. Along the way, we give an…

It is a well-known result of Etingof, Nikshych and Ostrik that there are finitely many inequivalent integral modular categories of any fixed rank $n$. This follows from a double-exponential bound on the maximal denominator in an Egyptian…

Let $\mathcal{F}(n)$ be the set of smooth Fano $n$-polytopes up to unimocular equivalence. In this paper, we consider the F-equivalence or I-equivalence classes for $\mathcal{F}(n)$ and introduce F-isolated or I-isolated smooth Fano…

In this article, we introduce the notion of mutation semigroup algebras. This concept simultaneously generalizes cluster algebras and semigroup algebras. We show that, under some mild conditions on the singularities, the spectrum $U={\rm…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is equivalent to the classification of simple semitoric systems…

We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical…

We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to…

The problem of classifying all unitary R-matrices of arbitrary finite dimension that have precisely two distinct eigenvalues is described, working up to a natural equivalence relation given by the characters of their braid group…