Related papers: The lonely runner conjecture holds for nine runner…

We give a short proof of the strong law of large numbers based on duality for random walk

We prove that deciding whether the Runner can win this turn (mate-in-1) in the Netrunner card game generalized to allow decks to contain an arbitrary number of copies of a card is weakly NP-hard. We also prove that deciding whether the Corp…

We prove that there is a matching between 2 intervals of positive integers of the same even length, with corresponding pairs coprime, provided the intervals are in $[n]$ and their lengths are $>c(\log n)^2$, for a positive constant $c$.…

We prove the Aharoni Berger Conjecture

We provide new sufficient conditions under which Ryser's conjecture holds.

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper we prove that this conjecture is true. That is, there exists a constant $b_0>0$ such that $R(K)\ge…

The Wiegold conjecture holds for the small Ree groups for $k$-tuples where $k \geq 5$.

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

We show that Dejean's conjecture holds for n>=27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

Eight combinatorial identities are listed and proved by counting paths in the one-dimensional random walk. Four of these identities are assumed to be new.

The Levin conjecture was proposed by Levin in 1962 which conjectures the solvability of any group equation with coefficients in a torsion free group. The Levin conjecture is recently shown to hold for group equations of length seven by…

Physical activity is known to help improve and maintain one's health. In particular, recreational running has become increasingly popular in recent years. Yet, lack of motivation often interferes with people's routines and thus may prohibit…

The work takes another look at the number of runs that a string might contain and provides an alternative proof for the bound. We also propose another stronger conjecture that states that, for a fixed order on the alphabet, within every…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

For a subtorus $T \subseteq (\mathbb{R}/\mathbb{Z})^n$, let $D(T)$ denote the $L^\infty$-distance from $T$ to the point $(1/2, \ldots, 1/2)$. For a subtorus $U \subseteq (\mathbb{R}/\mathbb{Z})^n$, define $\mathcal{S}_1(U)$, the Lonely…

For a long time, Collatz Conjecture has been assumed to be true, although a formal proof has eluded all efforts to date. In this article, evidence is presented that suggests such an assumption is incorrect. By analysing the stopping times…

We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.