Related papers: On the totally positive grassmannian
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmetic-geometric mean.
In this paper, we study the existence of positive entire large and bounded radial positive solutions for a nonlinear system. Our results give an answer of the question raised in [11].
We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.
We define dual equivalence for any collection of combinatorial objects endowed with a descent set, and we show that giving a dual equivalence establishes the symmetry and Schur positivity of the quasi-symmetric generating function. We give…
The real Grassmannian is both a projective variety (via Pl\"ucker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develop the commutative algebra of the latter variety. We…
The completeness of Gaussians in a Hilbert functional space is established
We propose a model theoretic interpretation of the theorems about the equivalence between mixed characteristic perfectoid spaces and their tilts.
A matrix is totally positive if all of its minors are positive. This notion of positivity coincides with the type A version of Lusztig's more general total positivity in reductive real-split algebraic groups. Since skew-symmetric matrices…
We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over…
The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix…
It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.
We verify in an elementary way a result of Peterson for the maximal orthogonal and Lagrangian Grassmannians, and then find Vafa-Intriligator type formulas which compute their 3-point, genus zero Gromov-Witten invariants. Finally we study…
We give another proof of a theorem of Fife - understood broadly as providing a finite automaton that gives a complete description of all infinite binary overlap-free words. Our proof is significantly simpler than those in the literature. As…
Complete non-ambiguous trees have been studied in various contexts. Recently, a conjecture was made about their determinants, and subsequently proved by Aval. An alternative proof is given here.
We introduce the notion of fully Hilbertian fields, a strictly stronger notion than that of Hilbertian fields. We show that this class of fields exhibits the same good behavior as Hilbertian fields, but for fields of uncountable…
We give a complete self-contained proof of Statman's finite completeness theorem and of a corollary of this theorem stating that the $\lambda$-definability conjecture implies the higher-order matching conjecture.
A rectangular matrix is called totally positive, if all its minors are positive. A point of a real Grassmanian manifold $G_{l,m}$ of $l$-dimensional subspaces in $\mathbb R^m$ is called strictly totally positive, if one can normalize its…
We prove the (equivariant) noetherian property for a wide class of varieties generalizing the class of Plucker varieties (Theorem 1). It improves previous results of Draisma-Eggermont who treated the case of bounded Plucker varieties. Key…
In this note we answer a question of Kunen (15.13 [Mi91]) showing that it is consistent that there are full Souslin trees