Related papers: Combinatorics of reductions between equivalence re…

In this paper, we explore combinatorial properties of the posets associated with Kohnert polynomials. In particular, we determine a sufficient condition guaranteeing when such ``Kohnert posets'' are bounded and two necessary conditions for…

In this commentary, we highlight the importance of: (1) carefully considering and clarifying whether a marginal or conditional treatment effect is of interest in a population-adjusted indirect treatment comparison; and (2) developing…

In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…

We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…

We derive a collection of separability conditions for bipartite systems of dimensions d X d which is based on the entropic version of the uncertainty relations. A detailed analysis of the two-qubit case is given by comparing the new…

Equality saturation is a powerful technique for program optimization. Contextual equality saturation extends this to support rewrite rules that are conditioned on where a term appears in an expression. Existing work has brought contextual…

There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also…

Necessary and sufficient conditions are derived for a social choice correspondence to be the one that selects the Pareto optimal alternatives.

If E is an equivalence relation Borel reducible to E_1 \times E_3 then either E is Borel reducible to the equality of countable sets of reals or E_1 is Borel reducible to E. The "either" case admits further strengthening.

In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on moment matrices (if criteria depend on designs via moment matrices) or with respect to the designs…

We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…

In contrast to common opinion, it is shown that equilibrium constants determine the time-dependent behavior of particular ratios of concentrations for any system of reversible first-order reactions. Indeed, some special ratios actually…

We introduce an equivalence relation on the set of Dyck paths and some operations on them. We determine a formula for the cardinality of those equivalence classes and use this information to obtain a combinatorial formula for the number of…

We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…

We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…

Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's…

The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…

The relationship according to which one physical theory encompasses the domain of empirical validity of another is widely known as "reduction." Here it is argued that one popular methodology for showing that one theory reduces to another,…