Related papers: A combinatorial approach to central to theorem

The centre of the symmetric group algebra $\mathbb{C}[\mathfrak{S}_n]$ has been used successfully for studying important problems in enumerative combinatorics. These include maps in orientable surfaces and ramified covers of the sphere by…

We provide a constructive treatment of basic results in the theory of central simple algebras. One main issue is the fact that one starting result, Wedderburn's Theorem stating that a simple algebra is a matrix algebra over a skew field, is…

Hindman's celebrated Finite Sums Theorem, and its high-dimensional version due to Milliken and Taylor, are extended from covers of countable sets to covers of arbitrary topological spaces with Menger's classic covering property. The methods…

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We…

This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a…

In the theory of zero-dimensional systems and their relation to $C^*$-algebras, Poon (1990) introduced a class of closed sets. We call the closed sets quasi-sections. Medynets (2006) introduced basic sets that are part of quasi-sections in…

We give a new proof of the Kat\v{e}tov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredient is how the ring of bounded continuous real-valued…

We make progress on two interrelated problems at the intersection of geometric measure theory, additive combinatorics and harmonic analysis: the discretised sum-product problem, and the dimension of Furstenberg sets. Along the way, we…

In this article, we investigate the image and preimage of the important combinatorial sets such as central sets, $C$-sets, and $J_\delta$-sets which play an important role in the study of combinatorics under certain partial semigroup…

Let X be a building of arbitrary type. A compactification $C_r(X)$ of the set Res(X) of spherical residues of X is introduced. We prove that it coincides with the horofunction compactification of Res(X) endowed with a natural combinatorial…

Two of the pillars of combinatorics are the notion of choosing an arbitrary subset of a set with $n$ elements (which can be done in $2^n$ ways), and the notion of choosing a $k$-element subset of a set with $n$ elements (which can be done…

In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…

This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…

We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the…

In 1978 Kostant suggested the Whittaker model of the center of the universal enveloping algebra U(g) of a complex simple Lie algebra g. The main result is that the center of U(g) is isomorphic to a commutative subalgebra in U(b), where b is…

Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated…

We present the basic theory of central subsets of semigroups from the nonstandard perspective. A key feature of this perspective is the replacement of the algebra of ultrafilters with the algebra of elements of iterated hyperextensions, a…

In this paper, we present a generalization of the parameterization method, introduced by Cabr\'{e}, Fontich and De la Llave, to center manifolds associated to non-hyperbolic fixed points of discrete dynamical systems. As a byproduct, we…