Related papers: A Counter Example To the Hodge Conjecture
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of…
We will give a simple proof of the ambiguous class number formula.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…
In this short paper we review and extract some features of the Fredholm Alternative problem .
The Hodge theory of complex algebraic varieties is at heart a transcendental comparison of two algebraic structures. We survey the recent advances bounding this transcendence, mainly due to the introduction of o- minimal geometry as a…
After reconsidering the Dasbach-Hougardy counterexample to the Kauffman Conjecture on alternating knots, we reformulate the conjecture and consider Dasbach-Hougardy counterexample and similar counterexamples in the light of the reformulated…
In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].
The $abc$ conjecture is a very deep concept in number theory with wide application to many areas of number theory. In this article we introduce the conjecture and give examples of its applications. In particular we apply the $abc$…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
New cases of the multiplicity conjecture are considered.
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results