24 citations · 30 across the 8 of their papers we have counts for
4 papers · 1 filter
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…