Related papers: Ulam Sets in New Settings
We introduce LAM, a subsystem of IMALL2 with restricted additive rules able to manage duplication linearly, called linear additive rules. LAM is presented as the type assignment system for a calculus endowed with copy constructors, which…
In this paper, we consider a generalization of Horadam sequence {w_n} which is defined by the recurrence w_n = aw_n-1 + cw_n-2; if n is even, w_n = bw_n-1 + cw_n-2; if n is odd with arbitrary initial conditions w_0, w_1 and nonzero real…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
Cameron introduced a bijection between the set of sum-free sets and the set of all zero-one sequences. In this paper, we study the sum-free sets of natural numbers corresponding to certain zero-one sequences which contain the Cantor-like…
We prove that in a large collection of naturally defined sets of permutations of fixed length, the numbers of permutations at Ulam distance k from the identity form a log-concave sequence in k.
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…
We develop invariant theory for the quantum group ${\rm U}_q$ of $G_2$ at generic $q$ in the setting of braided symmetric algebras. Let ${\mathcal A}_m$ be the braided symmetric algebra over $m$-copies of the $7$-dimensional simple ${\rm…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
Let $A$ be a subset of the cyclic group $\mathbf{Z}/p\mathbf{Z}$ with $p$ prime. It is a well-studied problem to determine how small $|A|$ can be if there is no unique sum in $A+A$, meaning that for every two elements $a_1,a_2\in A$, there…
Regular sound correspondences constitute the principal evidence in historical language comparison. Despite the heuristic focus on regularity, it is often more an intuitive judgement than a quantified evaluation, and irregularity is more…
We investigate temporal correlations in the simplest measurement scenario, i.e., that of a physical system on which the same measurement is performed at different times, producing a sequence of dichotomic outcomes. The resource for…
We obtain the asymptotic behaviour of the longest increasing/non-decreasing subsequences in a random uniform multiset permutation in which each element in {1,...,n} occurs k times, where k may depend on n. This generalizes the famous…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…
The $2$-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results on the $N$th $2$-adic complexity of any promising candidate for a pseudorandom sequence of finite length $N$ or…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over $\{0,1\}$ without two consecutive 1. Given a set $X$ of integers such that the language of…
A boolean term order is a total order on subsets of [n]={1,...,n} such that \emptyset < alpha for all nonempty alpha contained in [n], and alpha < beta implies alpha \cup gamma < beta \cup gamma for all gamma which do not intersect alpha or…
Generative molecular design has moved from proof-of-concept to real-world applicability, as marked by the surge in very recent papers reporting experimental validation. Key challenges in explainability and sample efficiency present…