Related papers: On the totally positive grassmannian

We prove a double binomial sum identity which differs from most binomial sum identities in that the summands involve the absolute value function. The identity is of interest because it can be used in proofs of lower bounds for the Hadamard…

Motivated by a question of Di Nasso, we prove that Hindman's theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic.

We prove that any quasigroup admissing complete or quasicomplete mapping has a prolongation to a quasigroup having one element more.

We prove several extensions of the Erdos-Fuchs theorem.

Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…

Andrews once gave $q$-analogues of a binomial congruence of Glaisher, and he suggested perfect $q$-analogues. In this note we give ones meeting the demand of Andrews.

We exhibit an identity that plays the same role as Vaughan's identity but is arguably simpler

We offer elementary proofs for fundamental properties of solutions to the homogeneous second Painlev\'e equation.

After reviewing the entropy power, the McKean, and the Gaussian completely monotone conjectures, we prove that the first implies the second, for each order of the time-derivative. The proof is elementary and is based on manipulating the…

We establish a form of the h-principle for the existence of foliations quasi-complementary to a given one; the same methods also provide a proof of the classical Mather-Thurston theorem.

We develop the version of the $J$-invariant for hermitian forms over quadratic extensions in a similar way Alexander Vishik did it for quadratic forms. This discrete invariant contains informations about rationality of algebraic cycles on…

Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…

A decidability proof for bisimulation equivalence of first-order grammars is given. It is an alternative proof for a result by S\'enizergues (1998, 2005) that subsumes his affirmative solution of the famous decidability question for…

We present a relative form of the Toponogov comparison theorem.

A generalization of the law of total covariance is presented and proved.

Motivated by Ziegler's computability-theoretic characterisation of finite absolute presentability between groups, we prove an analogous theorem in symbolic dynamics. We introduce the notion of one subshift being finitely determined over…

We show that several classical Ramseyan statements, and a forcing statement, are each equivalent to having Rothberger's property in all finite powers.

In this note, we present two new identities for derangements. As a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.

A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…

The aim of this note is to give a simpler proof of a result of Avsec, which states that $q$-Gaussian algebras have the complete metric approximation property.