Related papers: Thue, Combinatorics on words, and conjectures insp…
We extend the study of \emph{melonic} quartic tensor models to models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and iterated…
In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.
This paper is devoted to the study of the log-convexity of combinatorial sequences. We show that the log-convexity is preserved under componentwise sum, under binomial convolution, and by the linear transformations given by the matrices of…
Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…
We show how a commutative monad gives rise to a theory of extensive quantities, including (under suitable further conditions) a differential calculus of such. The relationship to Schwartz distributions is dicussed. The paper is a companion…
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
Scientific paper is devoted to establish connection of T-matrix - matrix of composite numbers 6h+1 v 6h-1 in special view - with Legendre's conjecture.
In this article, first we generalize the Thue-Morse sequence $(a(n))_{n=0}^\infty$ (the generalized Thue-Morse sequences) by a cyclic permutation and $k$ -adic expansion of natural numbers, and consider the necessary-sufficient condition…
Following a recent paper of Anselmo et al., we consider $m \times n$ rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved with a finite automaton. We also generalize the result to…
We define and study the Plancherel-Hecke probability measure on Young diagrams; the Hecke algorithm of [Buch-Kresch-Shimozono-Tamvakis-Yong '06] is interpreted as a polynomial-time exact sampling algorithm for this measure. Using the…
E. Sk\"oldberg's Morse Theory from an Algebraic Viewpoint and M. J\"ollenbeck's Algebraic Discrete Morse Theory and Applications to Commutative Algebra, which is the algebraic generalization of R. Forman's discrete Morse Theory for Cell…
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
We prove new general results on sumsets of sets having Szemer\'edi--Trotter type. This family includes convex sets, sets with small multiplicative doubling, images of sets under convex/concave maps and others.
Direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. We show that every linear Euler sum can be decomposed into a…
We prove a conjecture of Sturmfels, Timme and Zwiernik on the ML-degrees of linear covariance models in algebraic statistics. As in our previous works on linear concentration models, the proof ultimately relies on the computation of certain…
We survey recent developments on the Restriction conjecture.
This version is a significant improvement of the original paper. It includes a new section where we discuss norm tori in some detail. The new abstract is the following: In this paper we obtain Chevalley's ambiguous class number formula for…
Given a link or a tangle diagram, we define algorithmic Morse theoretic simplifications on their Khovanov homology. In contrast to Bar-Natan's scanning algorithm, the cancellations are postponed until the end and performed in one go.…
Studying and comparing arithmetic properties of a given automatic sequence and the sequence of coefficients of the composition inverse of the associated formal power series (the formal inverse of that sequence) is an interesting problem.…
We consider a numeration system in the ring of integers ${\mathcal O}_K$ of a number field, which we assume to be principal. We prove that the property of being a prime in ${\mathcal O}_K$ is decorrelated from two fundamental examples of…