Related papers: The Induced Bipartite Ramsey Theorem: An Expositio…
In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions that homogenize colorings over…
In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.
The main results of this paper (a) extend the finite Ramsey partition theorem, and (b) employ this extension to obtain a stronger form of the infinite Nash-Williams partition theorem, and also a new proof of Ellentuck's, and hence…
In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR. First, we find a natural obstruction in a finite group for not admitting a bipartite GRR. Then we give a complete…
We prove a conjecture that arose in the context of a subspace enumeration problem over finite fields. We prove, more generally, a bibasic, double-sum identity, which extends a $q$-analogue of the (terminating) binomial theorem.
We consider the restriction of Ramsey's theorem that arises from considering only translation-invariant colourings of pairs, and show that this has the same strength (both from the viewpoint of Reverse Mathematics and from the viewpoint of…
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
An approach to induction is presented, based on the idea of analysing the context of a given problem into `circumstances'. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that…
We give a categorical account of Arrow's theorem, a seminal result in social choice theory.
We present a powerful theorem for proving the irreducibility of tempered unitary representations of the free group.
In this contribution we present a concise introduction to quantum entanglement in multipartite systems. After a brief comparison between bipartite systems and the simplest non-trivial multipartite scenario involving three parties, we review…
We obtain simple proofs of certain inequalites for bivariate means.
An technically interesting proof of a known theorem.
Let $\mathbf{k}$ denote the totally ordered set (or chain) on $k$ elements. The product $\mathbf{k}^t=\mathbf{k}\times\cdots\times\mathbf{k}$ is a poset called a grid. This paper discusses several loosely related results on the Ramsey…
We expose the information flow capabilities of pure bipartite entanglement as a theorem -- which embodies the exact statement on the `seemingly acausal flow of information' in protocols such as teleportation. We use this theorem to…
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
We prove several results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected…
We prove a connectedness result for products of weighted projective spaces.
The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.
A vector variational principle is proved.