Related papers: On stable and fixed polynomials

Given a rational monomial map, we consider the question of finding a toric variety on which it is algebraically stable. We give conditions for when such variety does or does not exist. We also obtain several precise estimates of the degree…

We formulate a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra, and verify it for all torus knots and all simple Lie algebras…

We consider the equation $P(Q(x_1,\ldots,x_\nu))=Q(P(x_1),\ldots,P(x_\nu))$ in polynomials over the field of complex numbers and prove that if ${\rm deg}(P)>1$, then it is only solvable in polynomials that are affinely conjugate to…

We give sufficient conditions for a predicate P in a complete theory T to be stably embedded: P with its induced 0-definable structure has "finite rank", P has NIP in T and P is 1-stably embedded. This generalizes recent work by Hasson and…

We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for…

This paper consists of two related parts. In the first part we give a self-contained proof of homological stability for the spaces C_n(M;X) of configurations of n unordered points in a connected open manifold M with labels in a…

This paper explores a natural action of the group $\mathrm{PGL}_2(\mathbb F_q)$ on the set of monic irreducible polynomials of degree at least two over a finite field $\mathbb F_q$. Our main results deal with the existence and number of…

We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…

We prove in this note a stabilized version of a conjecture on $\A^1$-connectedness. For the stabilized version of this conjecture, we introduce the notion of stable $\A^1$-connectedness, which is can be seen as the stabilization of…

We introduce and study the notion of conic stability of multivariate complex polynomials in $\mathbb{C}[z_1,\ldots, z_n]$, which naturally generalizes the stability of multivariate polynomials. In particular, we generalize Borcea's and…

We study systems of equations of the form X1 = f1(X1, ..., Xn), ..., Xn = fn(X1, ..., Xn), where each fi is a polynomial with nonnegative coefficients that add up to 1. The least nonnegative solution, say mu, of such equation systems is…

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Specifically, given a stable matching $M_1$, a set $Q$ of forced pairs, and a set $P$ of forbidden pairs, we want to find a stable matching that includes…

Let $R$ be a two-dimensional regular local ring. In this paper, we prove that there is a bijection between the set of all valuations of $Quot(R)$ centered at $R$ and valuations of $k(x,y)$ centered at $k[x,y]_{(x,y)}$, where $k$ is the…

We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…

We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.

We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only…

A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…

Let $D_n$ be the dihedral group with $2n$ elements, and suppose $n$ is greater than one. We call ring system a finite $D_n$-symmetric set of points in $\mathbb{R}^2$. Ring systems have been used as models for planets surrounded by rings,…

For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a polynomial dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility…

Let X be a normal complex projective variety with at worst klt singularities, and L a big line bundle on X. We use valuations to study the log canonical threshold of L, as well as another invariant, the stability threshold. The latter…