Related papers: The non-decreasing condition on g-vectors
A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…
We give an example of a cluster-tilted algebra A with quiver Q, such that the associated cluster algebra has a denominator vector which is not the dimension vector of any indecomposable A-module. This answers a question posed by T.…
We prove explicit lower bounds for the smallest singular value and upper bounds for the condition number of rectangular, multivariate Vandermonde matrices with scattered nodes on the complex unit circle. Analogously to the Shannon-Nyquist…
For each vector $x\in \ell^{\infty}$, we can define the non-empty compact set $L_x$ of accumulation points of $x$. Given an infinite subset $A$ of $\mathbb{N}\backslash\{1\}$, we can therefore investigate under which conditions on $A$, the…
In this paper, we introduce the enough $g$-pairs property for a principal coefficients cluster algebra, which can be understood as a strong version of the sign-coherence of the $G$-matrices. Then we prove that any skew-symmetrizable…
This paper introduces a geometric mechanics framework for constrained systems on principal bundles through \emph{compatible pairs} $(\mathcal{D}, \lambda)$, addressing fundamental challenges in gauge-constrained physical systems. We…
Self-interacting vectors are seeing a burst of interest where various groups demonstrated that the field evolution ends in finite time. Two nonequivalent criteria have been offered to identify this breakdown: (i) the vector constraint…
This is the second in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…
We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. After introducing a suitable class…
We show that for the family of complex reflection groups $G=G(m,p,2)$ appearing in the Shephard--Todd classification, the endomorphism ring of the reduced hyperplane arrangement $A(G)$ is a non-commutative resolution for the coordinate ring…
Let $G$ be a unimodular locally compact group. We define a property of irreducible unitary $G$-representations $V$ which we call c-temperedness, and which for the trivial $V$ boils down to F{\o}lner's condition (equivalent to the trivial…
The Green-Lazarsfeld Secant Conjecture is a generalization of Green's Conjecture on syzygies of canonical curves to the cases of arbitrary line bundles. We establish the Green-Lazarsfeld Secant Conjecture for curves of genus g in all the…
Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…
In the representation theory of finite-dimensional algebras, the study of projective presentations of maximal rank is closely related to the study of generically $\tau$-regular irreducible components of varieties of modules over such…
For an algebraic stack $\sX$ flat and of finite presentation over a scheme $S$, we introduce various notions of {\em relative connected components} and {\em relative irreducible components}. The main distinction between these notions is…
In this article, we study model-theoretic properties of algebraic differential equations of order $2$, defined over constant differential fields. In particular, we show that the set of solutions of a general differential equation of order…
We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the…
We give a general lower bound on the rank of matrices of the form $\rho(h) - I$ with $\rho : G \rightarrow GL({\mathbb F}^n)$ an irreducible representation of a finite group $G$. The main tool in the proof is a (strengthening) of a…
In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition…
Let X be a compact complex manifold whose anti-canonical line bundle is big. We show that X admits no non-trivial holomorphic vector fields if it is Gibbs stable (at any level). The proof is based on a vanishing result for measure…