Related papers: Permutation Arrays Under the Chebyshev Distance
We define a deterministic family of permutations generated by an alternating center-edge extraction process on the ordered set [n] = {1,2,...,n}. Starting from the ordered list (1,2,...,n), one repeatedly removes the median element or…
In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an…
Motivated by a problem in quantum field theory, we study the up and down structure of circular and linear permutations. In particular, we count the length of the (alternating) runs of permutations by representing them as monomials and find…
The Ulam's metric is the minimal number of moves consisting in removal of one element from a permutation and its subsequent reinsertion in different place, to go between two given permutations. Thet elements that are not moved create…
Random permutation set (RPS) is a recently proposed framework designed to represent order-structured uncertain information. Measuring the distance between permutation mass functions is a key research topic in RPS theory (RPST). This paper…
The process of data interpretation is always based on the implicit introduction of equivalence relations on the set of walks over the database. Every equivalence relation on the set of walks specifies a Markov chain describing the…
In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional…
Methods for stochastic trace estimation often require the repeated evaluation of expressions of the form $z^T p_n(A)z$, where $A$ is a symmetric matrix and $p_n$ is a degree $n$ polynomial written in the standard or Chebyshev basis. We show…
Pinching antennas is a novel flexible-antenna technology, which can be realized by employing small dielectric particles on a waveguide. The aim of this letter is to characterize the array gain achieved by pinching-antenna systems (PASS). A…
The spatial preferred attachment (SPA) model is a model for networked information spaces such as domains of the World Wide Web, citation graphs, and on-line social networks. It uses a metric space to model the hidden attributes of the…
Phased arrays have enabled advances in communications, sensing, imaging, and wireless power transfer. In all these applications, large apertures enable higher power, higher data rates, higher resolution, and complex functionalities, but are…
The idea of frequency diverse array (FDA) has been invigorated in the recent years by supposing to have the ability of stopping the electromagnetic wave propagation and producing secretive direct connections between distant points. However,…
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of…
Movable antenna (MA) array is a novel technology recently developed where positions of transmit/receive antennas can be flexibly adjusted in the specified region to reconfigure the wireless channel and achieve a higher capacity. In this…
We present a simple formula for the expected number of inversions in a permutation of size $n$ obtained by applying $t$ random (not necessarily adjacent) transpositions to the identity permutation. More general, for any finite irreducible…
We study $P(n,3)$, the size of the largest subset of the set of all permutations $S_n$ with minimum Kendall $\tau$-distance $3$. Using a combination of group theory and integer programming, we reduced the upper bound of $P(p,3)$ from…
Computing the reversal distances of signed permutations is an important topic in Bioinformatics. Recently, a new lower bound for the reversal distance was obtained via the plane permutation framework. This lower bound appears different from…
A universal word (u-word) for $d$-dimensional permutations of length $n$ is a 2-dimensional word with $d-1$ rows, any size $n$ window of which is order-isomorphic to exactly one permutation of length $n$, and all permutations of length $n$…
Our work is motivated by Bourque and Pevzner's (2002) simulation study of the effectiveness of the parsimony method in studying genome rearrangement, and leads to a surprising result about the random transposition walk on the group of…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…