Ivan Mitrofanov
We prove that the problem of deciding whether a given morphic sequence is uniformly recurrent is decidable. The proof uses decidability of HD0L periodicity problem, which was recently proved in papers of F.Durand and I.Mitrofanov.
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We describe a shorter algorithm for HD0L uniform recurrence problem
We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic sequences are primitive substitutive sequences.
We explore a family of nested recurrence relations with arbitrary levels of nesting, which have an interpretation in terms of fixed points of morphisms over a countably infinite alphabet. Recurrences in this family are related to a number of well-known sequences, including Hofstadter's G sequence and the Conolly and Tanny sequences. For a recurrence a(n) in this family with only finitely terms, we provide necessary and sufficient conditions for the limit a(n)/n to exist.
Antipowers in Uniform Morphic Words and the Fibonacci Word
本文推广了 Berger 和 Defant 关于均匀态射词中反幂存在的猜想，将其从二元字母表扩展到任意有限字母表，并刻画了例外情形，同时证明了斐波那契词满足该猜想。
A Padovan-automatic description of a nested recurrence
本文研究嵌套递推序列，通过贪心Padovan记数系统识别其结构，构造自动机验证递推，确定偏差界与偏移集，并给出显式态射表示及Lean形式化验证。
Block-counting sequences are not purely morphic
本文研究m进制展开中有限字出现次数模p构成的序列，提出快速生成算法，证明素数m下多数序列为m-一致但非纯形态，且对应幂级数在F_m(t)上为m次代数级数。
We introduce $(s,t)$-uniform simplicial complexes. We show that the lengths of spheres in minimal filling diagrams associated to loops in such complexes are the terms of certain recurrence relations. We study the limit of the ratio of the area of such spheres over their length as the radii of spheres grow. Besides we compute the average Gaussian curvature for vertices inside these spheres.
In this paper we introduce and study new notions of uniform recurrence in multidimensional words. A $d$-dimensional word is called \emph{uniformly recurrent} if for all $(s_1,\ldots,s_d)\in\mathbb{N}^d$ there exists $n\in\mathbb{N}$ such that each block of size $(n,\ldots,n)$ contains the prefix of size $(s_1,\ldots,s_d)$. We are interested in a modification of this property. Namely, we ask that for each rational direction $(q_1,\ldots,q_d)$, each rectangular prefix occurs along this direction in positions $\ell(q_1,\ldots,q_d)$ with bounded gaps. Such words are called \emph{uniformly recurren…
The Fibonacci numbers satisfy the famous recurrence $F_n = F_{n - 1} + F_{n - 2}$. The theory of C-finite sequences ensures that the Fibonacci numbers whose indices are divisible by $m$, namely $F_{mn}$, satisfy a similar recurrence for every positive integer $m$, and these recurrences have an explicit, uniform representation. We will show that $a(mn)$ has a uniform recurrence over $m$ for any C-finite sequence $a(n)$ and use this to automatically derive some famous summation identities.
Uniform Recurrence in the Motzkin Numbers and Related Sequences mod $p$
本文研究可表示为 Laurent 多项式常数项形式的 Motzkin 数等整数序列，刻画其模 $p$ 一致递归的素数，并将其余情形归约为性质良好的广义中心三项式系数。
A Linear Representation for Constant Term Sequences mod $p^a$ with Applications to Uniform Recurrence
本文刻画了常数项序列模素数幂的一致递归性，并引入新颖的线性表示，证明非一致递归时零的频率为1。
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other powers. This is motivated by similar results in number theory concerning additive basis of natural numbers. Moreover, motivated by a result of Kamae and Mendès-France, that links single recurrence with uniform distribution properties of sequences, we look for an analogous result dealing with higher order recurrence and make a related conjecture.
Analytic properties of Speyer's $g$-polynomial of uniform matroids
本文通过递归关系证明了均匀拟阵的Speyer $g$-多项式仅有实零点，并证明了其系数的渐近正态性。为拟阵理论提供了新的解析工具。
Factor-balancedness, linear recurrence, and factor complexity
本文研究了无限字的因子平衡性与线性递归关系，提出通用条件并构造了具有指数复杂度的因子平衡字示例。
We make three observations regarding a question popularized by Katznelson: is every subset of $\mathbb Z$ which is a set of Bohr recurrence is also a set of topological recurrence? (i) If $G$ is a countable abelian group and $E\subset G$ is an $I_0$ set, then every subset of $E-E$ which is a set of Bohr recurrence is also a set of topological recurrence. In particular every subset of $\{2^n-2^m : n,m\in \mathbb N\}$ which is a set of Bohr recurrence is a set of topological recurrence. (ii) Let $\mathbb Z^ω$ be the direct sum of countably many copies of $\mathbb Z$ with standard basis $E$. If e…
On the number of extension closed additive subcategories for uniformly oriented $A_n$ quivers
本文给出了计算OEIS序列A393920的递推公式，揭示了其与斐波那契数列的联系，并得到了其增长的指数上下界。
On the number of cokernel-closed additive subcategories for uniformly oriented $A_n$ quivers
研究一致定向 $A_n$ 箭图表示范畴中余核闭加法子范畴的计数序列，发现其与卡特兰数的联系并推导隐式递推，同时刻画了相关格的交不可约元素。
Suppose that $G_j$ is a sequence of finite connected planar graphs, and in each $G_j$ a special vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a distributional limit $G$ of such graphs. Assume that the vertex degrees of the vertices in $G_j$ are bounded, and the bound does not depend on $j$. Then after passing to a subsequence, the limit exists, and is a random rooted graph $G$. We prove that with probability one $G$ is recurrent. The proof involves the Circle Packing Theorem. The motivation for this work comes from the theory of random spherical triangulatio…
Avoiding 5/4-powers on the alphabet of nonnegative integers
本文刻画了非负整数字母表上避免5/4次幂的字典序最小词的结构，证明其具有特定形式，并由此得出字母序列的6-正则性（秩188），推广至一般递推关系的k-正则性。
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