ﻻ يوجد ملخص باللغة العربية
In this note, we show that a Toy Conjecture made by (Boyle, Ishai, Pass, Wootters, 2017) is false, and propose a new one. Our attack does not falsify the full (non-toy) conjecture in that work, and it is our hope that this note will help further the analysis of that conjecture. Independently, (Boyle, Holmgren, Ma, Weiss, 2021) have obtained similar results.
The Frankl conjecture (called also union-closed sets conjecture) is one of the famous unsolved conjectures in combinatorics of finite sets. In this short note, we introduce and to some extent justify some variants of the Frankl conjecture.
In this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontrivial, the dimension of the base is greater than the dimension of the
We use logarithmic {ell}-class groups to take a new view on Greenbergs conjecture about Iwasawa {ell}-invariants of a totally real number field K. By the way we recall and complete some classical results. Under Leopoldts conjecture, we prove that Gre
Let $G=(V(G), E(G))$ be a multigraph with maximum degree $Delta(G)$, chromatic index $chi(G)$ and total chromatic number $chi(G)$. The Total Coloring conjecture proposed by Behzad and Vizing, independently, states that $chi(G)leq Delta(G)+mu(G) +1$ f
In this short note we confirm the relation between the generalized $abc$-conjecture and the $p$-rationality of number fields. Namely, we prove that given K$/mathbb{Q}$ a real quadratic extension or an imaginary $S_3$-extension, if the generalized $ab