Related papers: Partition relations for Hurewicz-type selection hy…

We identify computability-theoretic properties enabling us to separate various statements about partial orders in reverse mathematics. We obtain simpler proofs of existing separations, and deduce new compound ones. This work is part of a…

We describe the second homotopy group of any CW-complex $K$ by analyzing the universal cover of a locally finite model of $K$ using the notion of $G$-coloring of a partially ordered set. As applications we prove a generalization of the…

We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in terms of certain ultrafilters related to tensor products…

This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is…

We introduce a universal approach for applying the partition rank method, an extension of Tao's slice rank polynomial method, to tensors that are not diagonal. This is accomplished by generalizing Naslund's distinctness indicator to what we…

Starting from the characteristic polynomial for ordinary matrices we give a combinatorial deduction of the Mandelstam identities and viceversa, thus showing that the two sets of relations are equivalent. We are able to extend this…

We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived…

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.

In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.

We develop a Van der Waerden type theorem in an axiomatic setting of graded lattices and show that this axiomatic formulation can be applied to various lattices, for instance the set partition and the Boolean lattices. We derive the…

From a machine learning point of view, identifying a subset of relevant features from a real data set can be useful to improve the results achieved by classification methods and to reduce their time and space complexity. To achieve this…

Feature selection methods are usually evaluated by wrapping specific classifiers and datasets in the evaluation process, resulting very often in unfair comparisons between methods. In this work, we develop a theoretical framework that…

We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…

This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.

We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…

A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new…

We prove additive and multiplicative partition theorems, obtaining combinatorial results for p-quasicyclic groups, where p is a prime number. We also get density results for p-quasicyclic groups via left F{\o}lner sequences of non-empty…

A two-parameter family of exchangeable partitions with a simple updating rule is introduced. The partition is identified with a randomized version of a standard symmetric Dirichlet species-sampling model with finitely many types. A…

In this note we establish a Ramsey-type result for certain subsets of the $n$-dimensional cube. This can then be applied to obtain reasonable bounds on various related structures, such as (partial) Hales-Jewett lines for alphabets of sized…

Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the…