Related papers: On the totally positive grassmannian

We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.

A doubly nonnegative matrix can be written as a Gramian matrix, and a completely positive matrix can therefore be written as a Gramian matrix of some nonnegative vectors. In this paper, we introduce Gramian tensors and study 2-dimension…

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

We give an elementary and self-contained proof of the equivalence of a collection of Wolstenholme-type congruences due to Helou and Terjanian.

In this paper we prove the equivalence of two definitions of laminated currents.

We provide an alternative proof that the finite rational linear combination of radicals, under certain constraint, are linearly independent over $\mathbb{Q}$.

We answer a question of Zadrozny.

New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.

A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.

We introduce the notion of a probabilistic identity of a residually finite group. We prove that a finitely generated linear group satisfies a probabilistic identity if and only if it is virtually solvable. As an application, we prove a…

We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We…

We give a uniform proof of a significant part of the Cachazo-Douglas-Seiberg-Witten conjecture by using topology and geometry of infinite Grassmannians.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.

In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert $A$-modules over locally $C^{*}$-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring…

We study $\Sigma^1_2$ definable counterparts for some algebraic equivalent forms of the Continuum Hypothesis. All turn out to be equivalent to "all reals are constructible".

In this paper, we prove a criterion of elementary equivalence of stable linear groups over fields of characteristic two.

In 1993, E. Lesigne proved a polynomial extension of the Wiener-Wintner ergodic theorem and asked two questions: does this result have a uniform counterpart and can an assumption of total ergodicity be replaced by ergodicity? The purpose of…

We prove a new family of total positivity criteria for partial flag varieties for simply-connected complex algebraic group in the simply laced case.