Related papers: The $S$-adic Pisot conjecture on two letters

The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and…

There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of two letters/tiles. Furthermore, we obtain…

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

Fekete, Jord\'an and Kaszanitzky [4] characterised the graphs which can be realised as 2-dimensional, infinitesimally rigid, bar-joint frameworks in which two given vertices are coincident. We formulate a conjecture which would extend their…

We propose exact $S$-matrices for the AdS_3/CFT_2 duality between Type IIB strings on AdS_3 x S^3 x M_4 with M_4=S^3 x S^1 or T^4 and the corresponding two-dimensional conformal field theories. We fix the complete two-particle S-matrices…

We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explicit construction of a fundamental domain with fractal…

Inspired by a Zudilin-Zhao's supercongruences pattern related to Ramanujan-like series for $1/\pi^k$, we conjecture a kind of $p$-adic expansions.

We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.

An idea that became unavoidable to study zero entropy symbolic dynamics is that the dynamical properties of a system induce in it a combinatorial structure. An old problem addressing this intuition is finding a structure theorem for…

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

Every graph G can be embedded in a Euclidean space as a two-distance set. This allows us to reformulate the analogue of Borsuk's conjecture for two-distance sets in terms of graphs. This conjecture remains open for dimensions from 4 to 63.…

We study the Mathieu Conjecture for $SU(2)$ using the matrix elements of its unitary irreducible representations. We state a conjecture for the particular case $SU(2)$ implying the Mathieu Conjecture for $SU(2)$.

We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…

In this short note we expand on recent results on the degenerate principle series $I(s,\chi)$ of classical groups associated to $s\in \mathbb{C}$ and a quadratic character $\chi$. In particular, we strengthen the result for $s\in…

Pseudo-effect algebras are partial algebraic structures, that were introduced as a non-commutative generalization of effect algebras. In the present paper, lattice ordered pseudo-effect algebras are considered as possible algebraic…

In 2001, Woodall conjectured that for every pair of integers $s,t \ge 1$, all graphs without a $K_{s,t}$-minor are $(s+t-1)$-choosable. In this note we refute this conjecture in a strong form: We prove that for every choice of constants…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We prove that the $abc$-Conjecture implies upper bounds on Zsigmondy sets that are uniform over families of unicritical polynomials over number fields. As an application, we use the $abc$-Conjecture to prove that there exist uniform bounds…

The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).

In this paper, we consider a conjecture of Erdos and Rosenfeld and a conjecture of Ruzsa when the number is an almost square. By the same method, we consider lattice points of a circle close to the x-axis with special radii.