Related papers: Some remarks on permanent dominant conjecture
We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to…
Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also…
In this article, we define a very important sequence of functions, all the functions of this sequence present behaviors very close to that of the Collatz function. The study of such functions allows us to obtain very interesting results…
We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the…
We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…
A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in l_p is attained either for the identity matrix I or for a constant…
We introduce more properties of forcing notions which imply that their lambda-support iterations are lambda-proper, where lambda is an inaccessible cardinal. This paper is a direct continuation of section A.2 of math.LO/0210205. As an…
We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…
We introduce a new notion of the determinant, called symmetrized determinant, for a square matrix with the entries in an associative algebra $\AA$. The monomial expansion of the symmetrized determinant is obtained from the standard…
We provide a universal characterization of the construction taking a scheme $X$ to its stable $\infty$-category $\text{Mot}(X)$ of noncommutative motives, patterned after the universal characterization of algebraic K-theory due to…
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing…
Many invariants of finitely generated positive cancelative commutative semigroups can be studied from their Poincar\'e series. We offer and present several closed formulas for them. Moreover, those formulas have elementary proofs and are…
Starting from the expression for the superdeterminant of $ (xI-M)$, where $M$ is an arbitrary supermatrix , we propose a definition for the corresponding characteristic polynomial and we prove that each supermatrix satisfies its…
We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…
We give a combinatorial interpretation of the determinant of a matrix as a generating function over Brauer diagrams in two different but related ways. The sign of a permutation associated to its number of inversions in the Leibniz formula…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
Let $X$ be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of $X$: (1) $\mathsf{D}_{\mathrm{qc}}(X)$ is compactly generated by perfect complexes and (2) if $X$…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…