相关论文: Base 3/2 and Greedily Partitioned Sequences
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step toward a more general understanding of chaotic scattering in higher dimensions. Despite of the…
Consider the puzzle: given a number, remove $k$ digits such that the resulting number is as large as possible. Various techniques were employed to derive a linear-time solution to the puzzle: predicate logic was used to justify the…
We study the greedy (exploitation-only) algorithm in bandit problems with a known reward structure. We allow arbitrary finite reward structures, while prior work focused on a few specific ones. We fully characterize when the greedy…
In this problem, Alice and Bob, are provided $X_{1}^{n}$ and $X_{2}^{n}$ that are IID $p_{X_1 X_2}$. Alice and Bob can communicate to Charles over (noiseless) links of rate $R_1$ and $R_2$, respectively. Their goal is to enable Charles…
Elton's near unconditionality and quasi-greediness for largest coefficients are two properties of bases that made their appearance in functional analysis from very different areas of research. One of our aims in this note is to show that,…
We study the asymptotic behaviour of the trace (the sum of the diagonal parts) of a plane partition of the positive integer n, assuming that this parfition is chosen uniformly at random from the set of all such partitions.
Although the basic idea behind the concept of a greedy basis had been around for some time, the formal development of a theory of greedy bases was initiated in 1999 with the publication of the article [S.~V.~Konyagin and V.~N.~Temlyakov, A…
We construct a basis for free Lie algebras via a ``left-greedy'' bracketing algorithm on Lyndon-Shirshov words. We use a new tool -- the configuration pairing between Lie brackets and graphs of Sinha-Walter -- to show that the left-greedy…
We explain how fractional spin and statistics are relevant to (super)strings in a three-dimensional (3D) Minkowski spacetime.
We associate a sequence of positive integers, termed the type sequence, with a cochordal graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We then classify all positive integer $n$ such that the zero…
In this paper we present an extension of Stanley's theorem related to partitions of positive integers. Stanley's theorem states a relation between "the sum of the numbers of distinct members in the partitions of a positive integer $n$" and…
A popular graph clustering method is to consider the embedding of an input graph into R^k induced by the first k eigenvectors of its Laplacian, and to partition the graph via geometric manipulations on the resulting metric space. Despite…
We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recursion relations in the length of the chain. These relations…
We consider a variant on the Tetranacci sequence, where one adds the previous four terms, then divides the sum by two until the result is odd. We give an algorithm for constructing "initially division-poor" sequences, where over an initial…
We describe a canonical spanning tree of the ridge graph of a subword complex on a finite Coxeter group. It is based on properties of greedy facets in subword complexes, defined and studied in this paper. Searching this tree yields an…
We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the…
In this paper, we investigate properties of the fixed point sequence of the Josephus function $J_3$. First, we establish a connection between this sequence and the Chinese Remainder Theorem. Next, we identify a clear numerical pattern for…
In this paper, we perform an arithmetization of well-formed parenthesis strings with zeros (Motzkin words) and of corresponding Motzkin paths. The transformations used are reminiscent of G\"odel numbering for mathematical objects of some…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…