Related papers: Proofs of some Conjectures from the OEIS

We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…

Descents of odd length in Dyck paths are discussed, taking care of some variations. The approach is based on generating functions and the kernel method and augments relations about them from the Encyclopedia of Integer Sequences, that were…

This is a technical report, containing all the theorem proofs in paper "Link Identifiability in Communication Networks with Two Monitors" by Liang Ma, Ting He, Kin K. Leung, Ananthram Swami, and Don Towsley, published in IEEE Globecom,…

This article is dedicated to domino tilings of certain types of graph grids. For each of these grids, the domino tilings are represented using linear-recurrent sequences. New dependencies are proved that are not included in Neil Sloane's…

We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent…

This paper offers a proof of the Coase theorem by formalizing the notion of ideal exchanges.

Open information extraction (OIE) systems extract relations and their arguments from natural language text in an unsupervised manner. The resulting extractions are a valuable resource for downstream tasks such as knowledge base…

We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already…

With the abundant amount of available online and offline text data, there arises a crucial need to extract the relation between phrases and summarize the main content of each document in a few words. For this purpose, there have been many…

In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…

The paper investigates the properties of a nonlinear recursive sequence which includes several ones studied formerly in the literature.

We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.

We discuss some seemingly unrelated observations on integers, whose close or farther away neighbors show a complex of combinatorial, ordering, arithmetical or probabilistic properties, emphasizing puzzlement in more common expectations.

We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…

Nous rappelons l'historique de la demonstration de la conjecture des fibres de Seifert, ainsi que ses motivations et ses diverses generalisations. ----- We recall the history of the proof of the Seibert fiber space conjecture, as well as…

We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient…

We verify the Invariance Conjectures of tautological equations in genus two. In particular, a uniform derivation of all known genus two equations is given.

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.

This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof…

We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We first introduce a simple logical language which makes it possible to express that a fact causes another…