Related papers: A continuation of [DjSh:691]
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.
Three complementation-like involutions are constructed on permutations to prove, and in some cases generalize, all remaining fourteen joint symmetric equidistribution conjectures of Lv and Zhang. Further enumerative results are obtained for…
In this short note, we answer two questions of Chen and Ruzsa negatively and answer a problem of Ma and Chen affirmatively.
This paper reviews the progress reported at this Royal Society Discussion Meeting and advertizes some possible future directions in our drive to understand dark matter and dark energy. Additionally, a first attempt is made to place in…
An analysis of several important aspects of competition or conflict in games, social choice and decision theory is presented. Inherent difficulties and complexities in cooperation are highlighted. These have over the years led to a certain…
This is the final version of the 2007 preprint titled "On the derived category of 1-motives, I". It has been substantially expanded to contain a motivic proof of (two thirds of) Deligne's conjecture on 1-motives with rational coefficients,…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
Modulo the existence of large cardinals, there is a model of set theory in which for some set $B$ of regular cardinals, the sequence $\langle \text{pcf}^\alpha(B): \alpha \in \text{Ord} \rangle$ is strictly increasing. The result answers a…
Building on work by Dan-Cohen--Wewers, Dan-Cohen [DC], and Brown, we push the computational boundary of our explicit motivic version of Kim's method in the case of the thrice punctured line over an open subscheme of Spec ZZ. To do so, we…
The mood at this conference is summarized in David Hughes' comment, ``this decade will be amazing.'' We've just had a pretty good ten years of advances in cosmology and extragalactic astronomy; why should we expect a repeat, another decade…
In a self-contained way, we deal with revised countable support iterated forcing for the reals. We improve theorems on preservation of the property UP, weaker than semi proper, and we hopefully improve the presentation. We continue [Sh:b,…
In this paper we examinate some phenomena arising when a holomorphic germ is analytically continued.
I begin my discussion by giving an overview of the main results. Then I proceed to touch upon issues about whether the credible ball constructed can be interpreted as a confidence ball, suggestions on reducing computational costs, and…
We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…
We present a conjecture about partitions, with a very elementary formulation.
We survey the state of the union-closed sets conjecture.
We briefly comment on the paper "On the correlation between the local dark matter and stellar velocities" (Bozorgnia et al. 2018), which purports to test our previous claims regarding the correlation of stellar and dark matter kinematics…
In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal $\kappa \ge \omega_2$, $\textsf{ISP}(\kappa)$ implies that $\textsf{SCH}$ holds above $\kappa$, and (3) forcing posets…
We study a game where one player selects a random function, and the other has to guess that function, and show that with high probability the second player can correctly guess most of the random function. We apply this analysis to…