24 citations · 30 across the 8 of their papers we have counts for
10 papers
On rational approximation of algebraic functions
Julius Borcea, Rikard Bögvad, Boris Shapiro
We construct a new scheme of approximation of any multivalued algebraic function by a sequence of rational functions. The latter sequence is…
Classifying real polynomial pencils
Julius Borcea, Boris Shapiro
Let $\bP^n$ be the space of all homogeneous polynomials of degree in two variables with real coefficients. The standard discriminant $\D_{n+1}\subset \bP^n$ is Whitney stratifi…
Hyperbolic polynomials and spectral order
Julius Borcea, Boris Shapiro
The spectral order on $\bR$ induces a partial ordering on the manifold $\calH_{n}$ of monic hyperbolic polynomials of degree . We show that the semigroup $\tilde{\calS}$ generat…
Periodic de Bruijn triangles: exact and asymptotic results
B. Shapiro, M. Shapiro, A. Vainshtein
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic for…
Trees, parking functions, syzygies, and deformations of monomial ideals
Alexander Postnikov, Boris Shapiro
For a graph G, we construct two algebras, whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo…
A few riddles behind Rolle's theorem
B. Shapiro, M. Shapiro
We call a smooth function of one variable a degree n pseudopolynomial if its n-th derivative has no (real) zeros. An n pseudopolynomial is called hyperbolic if it has exactly n sim…