Related papers: When do Schubert polynomial products stabilize?
We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic…
We study the r-th elementary symmetric polynomial in $n$ variables with 2<r<n. There are two kinds of linear transformations on the parameter space that leave this polynomial invariant: Namely, any permutation of the variables and…
We initiate a quantitative study of Hilbert-Schmidt stability for infinitely presented groups through the novel notion of stability radius growth. We exhibit an uncountable family of Hilbert-Schmidt stable amenable groups with arbitrarily…
To any Schur polynomial $s_{\lambda}$ one can associated its derived polynomials $s_{\lambda}{(i)}$ $i=0,\ldots,|\lambda|$ by the rule $$s_{\lambda}(x_1+t,\ldots,x_n+t) = \sum_i s_{\lambda}^{(i)}(x_1,\ldots,x_n) t^i.$$ We conjecture that…
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…
A noncommutative polynomial is stable if it is nonsingular on all tuples of matrices whose imaginary parts are positive definite. In this paper a characterization of stable polynomials is given in terms of strongly stable linear matrix…
The shuffle product plays an important role in the study of multiple zeta values. This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two…
In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…
The Schubert vanishing problem is a central decision problem in algebraic combinatorics and Schubert calculus, with applications to representation theory and enumerative algebraic geometry. The problem has been studied for over 50 years in…
Polyak-Ruppert averaging yields an asymptotically normal estimator with sandwich covariance $H^{-1}SH^{-1}$, the foundation of online inference. When the gradient step is preconditioned by a data-driven matrix $P_t$, we ask how fast $P_t$…
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…
A polynomial has saturated Newton polytope (SNP) if every lattice point of the convex hull of its exponent vectors corresponds to a monomial. We compile instances of SNP in algebraic combinatorics (some with proofs, others conjecturally):…
We prove that, when $n$ goes to infinity, the expression, with respect to the dual Kazhdan-Lusztig basis, of the product $\hat{\underline{H}}_x\underline{H}_y$ of elements of the dual and the usual Kazhdan-Lusztig bases in the Hecke algebra…
This partly expository paper first supplies the details of a method of factoring a stable C*-algebra A as B \otimes K in a canonical way. Then it is shown that this method can be put into a categorical framework, much like the…
In this paper the space of almost commuting elements in a Lie group is studied through a homotopical point of view. In particular a stable splitting after one suspension is derived for these spaces and their quotients under conjugation. A…
We give an algorithm to compute stable commutator length in free products of cyclic groups which is polynomial time in the length of the input, the number of factors, and the orders of the finite factors. We also describe some experimental…
In recent years, there has been a considerable amount of interest in stability of equations and their corresponding groups. Here, we initiate the systematic study of the quantitative aspect of this theory. We develop a novel method,…
Using a new strategy, we extend the classical Nekhoroshev's estimates to the case of H\"older regular steep near-integrable hamiltonian systems, the stability times being polynomially long in the inverse of the size of the perturbation. We…
We carry on the investigation initiated in [15] : we describe new shuffle products coming from some special functions and group them, along with other products encountered in the literature, in a class of products, which we name…
Traditional formulations of geometric problems from the Schubert calculus, either in Plucker coordinates or in local coordinates provided by Schubert cells, yield systems of polynomials that are typically far from complete intersections and…