Related papers: Omitting unary and affine types

We prove identities for six infinite series whose values involve linear combinations of $\pi$ and $\operatorname{ln} 2$, that do not appear in standard infinite series references.

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…

We revise the enumeration of the imprimitive rank two quaternionic reflection groups, adding missing groups and establishing isomorphisms between groups in the published tables. The isomorphisms are obtained as a consequence of the…

The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity,…

Following a remark of Lawvere, we explicitly exhibit a particularly elementary bijection between the set T of finite binary trees and the set T^7 of seven-tuples of such trees. "Particularly elementary" means that the application of the…

A (positive definite integral) quadratic form is called almost 2-universal if it represents all (positive definite integral) binary quadratic forms except those in only finitely many equivalence classes. Oh [7] determined all almost…

What can we discover? As the discussion in this paper is limited to ontological considerations, it does not deal with the discovery of new concepts. It raises the following question: What are the entities or existents that we can discover?…

There exist two distinct types of ultrafilter extensions of binary relations, one discovered in universal algebra and modal logic, and another, in model theory and algebra of ultrafilters. We show that the extension of the latter type is…

This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal,…

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…

Consider a binary decision making process where a single machine learning classifier replaces a multitude of humans. We raise questions about the resulting loss of diversity in the decision making process. We study the potential benefits of…

In a paper by the first author it was shown that for certain arithmetical results on conjugacy class sizes it is enough to only consider the vanishing conjugacy class sizes. In this paper we further weaken the conditions to consider only…

There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of two letters/tiles. Furthermore, we obtain…

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of…

We present an algorithm, called the Offset Tree, for learning to make decisions in situations where the payoff of only one choice is observed, rather than all choices. The algorithm reduces this setting to binary classification, allowing…

This paper completes a project to enumerate permutations avoiding a triple T of 4-letter patterns, in the sense of classical pattern avoidance, for every T. There are 317 symmetry classes of such triples T and previous papers have…

For every pattern $p$ over the alphabet $\{x,y,x^R,y^R\}$, we specify the least $k$ such that $p$ is $k$-avoidable.

We say that a finite factor $f$ of a word $w$ is \emph{imaged} if there exists a non-erasing morphism $m$, distinct from the identity, such that $w$ contains $m(f)$. We show that every infinite word contains an imaged factor of length at…

In this note, we give an elementary proof of the following classical fact. Any positive definite ternary quadratic form over the rational numbers fails to represent infinitely many positive integers. For any ternary quadratic form (positive…

It is known that a $2\times 2$ quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher orders. In this paper a different point of view is adopted…