相关论文: A counterexample to the "composition conjecture"

Counterfactuals have been recognized as an effective approach to explain classifier decisions. Nevertheless, they have not yet been considered in the context of clustering. In this work, we propose the use of counterfactuals to explain…

In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…

The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.

We study the Hall and composition algebras of an affine quiver. In the case of a cyclic quiver, we provide generators for the central polynomial algebra described by Schiffmann and prove that this is in fact the whole of the centre of the…

The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…

We reduce the Nowicki conjecture on the Weitzenb\"ock derivation of polynomial algebras to well-known problem of the classical invariant theory.

We present an example of a symmetric tensor of size $800\times 800\times 800$ which can be written a sum of $903$ simple tensors with complex entries but not as a sum of $903$ symmetric simple tensors.

We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…

In this notes we describe the center and derivations of the Infinitesimal Hecke algebra of $sl_2$ by means of elementary computations.

In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing counterexamples to the Lavrentiev gap, which we apply to…

Following their resolution of the Erd\H{o}s $B+B+t$ problem, Kra Moreira, Richter, and Robertson posed a number of questions and conjectures related to infinite configurations in positive density subsets of the integers and other amenable…

Recently, F. Brenti put a preprint on the arXiv with several interesting open problems on Coxeter groups and unimodality. In this note, we refute one of these conjectures with a counterexample and provide supporting data related to it. This…

We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to…

For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…

About the relation between a counterexample in the theory of numbers constructible by ruler and compass, due to Ian Stewart, and Alhazen's problem concerning the circular mirror.

We address the conjectures left by the recent article by Ferreira et al. titled ``Commuting maps and identities with inverses on alternative division rings.'' We also present an example showing the necessity of the conditions of the results…

Some inverse problems for semi-infinite periodic generalized Jacobi matrices are considered. In particular, a generalization of the Abel criterion is presented. The approach is based on the fact that the solvability of the Pell-Abel…

We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem,…

We construct infinite classes of almost bent and almost perfect nonlinear polynomials, which are affinely inequivalent to any sum of a power function and an affine function.