Related papers: The $abc$ Conjecture implies the Weak Diversity Co…
A combinatorial identity that was needed in Ahlgren and Ono's proof of a certain congruence conjecture of Frits Beukers is stated, and a pointer to its WZ proof is given.
We show that the $abc$ conjecture of Masser-Oesterl\'{e}-Szpiro for number fields implies that there are infinitely many non-Fibonacci-Wieferich primes. We also provide a new heuristic for the number of such primes beneath a certain value.
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
In representation theory of finite groups, there is a well-known and important conjecture due to M. Brou\'e. He conjectures that, for any prime $p$, if a $p$-block $A$ of a finite group $G$ has an abelian defect group $P$, then $A$ and its…
In this short note we reduce the b-semiampleness conjecture for lc-trivial fibrations to the b-semiampleness conjecture for klt-trivial fibrations.
We answer a question of Usuba by showing that the combinatorial principle $UB_\lambda$ can fail at a singular cardinal. Furthermore, $\lambda$ can be taken to be $\aleph_\omega.$
We prove Union-Closed sets conjecture.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
Several results about the union-closed sets conjecture are presented.
We prove the Aharoni Berger Conjecture
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur's Inequality for all split and quasi-split (connected) reductive groups. These results are related to the non-emptiness of certain affine Deligne-Lusztig…
This paper treats what we call `weak geometric liftings' of Galois representations associated to abelian varieties. This notion can be seen as a generalization of the idea of lifting a Galois representation along an isogeny of algebraic…
A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid.
We prove that the approximation conjecture of Luck holds for all amenable groups in the complex group algebra case. This result was previously proved by Dodziuk, Linnell, Mathai, Schick and Yates under the assumption that the group is…
We prove two weak compactness criteria in Musielak-Orlicz spaces for $N$-functions satisfying the $\Delta_2$-condition. They extend criteria from And\^o for Orlicz spaces to this setting of non-symmetrical Banach function spaces. As…
We represent preferences that exhibit absolute or relative attitudes towards ambiguity without assuming convexity of preferences. Our analysis is motivated by the recent experimental evidence by Baillon and Placido (2019) indicating that…
We prove two conjectures of Paule and Radu from their recent paper on broken k-diamond partitions.
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
This Paper investigate sequent calculi for certain weak subintuitionistic logics. We establish that weakening and contraction are height-preserving admissible for each of these calculi, and we provide a syntactic proof for the admissibility…
In this paper, we introduce and investigate the concepts of cyclically weakly amenable and point amenable. Then, we compare these concepts with the concepts of weakly amenable and cyclically amenable and find the relation between them. For…