Related papers: On minimal pattern-containing inversion sequences
Borradaile et al. (2017) investigated orientations of an undirected graph in which the sequence of in-degrees of the nodes is lexicographically minimal, which we call decreasingly minimal (=dec-min). They proved that an orientation is…
A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If the pair of matrices are the same, they define a dual relationship. Here presented is a unified approach to construct dual relationships via…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
Consider a finite set of sources, each producing i.i.d. observations that follow a unique probability distribution on a finite alphabet. We study the problem of matching a finite set of observed sequences to the set of sources under the…
A permutation is defined to be cycle-up-down if it is a product of cycles that, when written starting with their smallest element, have an up-down pattern. We prove bijectively and analytically that these permutations are enumerated by the…
Basis pursuit is the problem of finding a vector with smallest $\ell_1$-norm among the solutions of a given linear system of equations. It is a well-known convex relaxation of the sparse affine feasibility problem, where sparse solutions to…
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. The authors of [2] showed that the expected number of distinct consecutive patterns of all lengths $k\in\{1,2,\ldots,n\}$ in $\pi_n$ was $\frac{n^2}{2}(1-o(1))$ as $n\to\infty$,…
There are many practical applications that require simplification of polylines. Some of the goals are to reduce the amount of information necessary to store, improve processing time, or simplify editing. The simplification is usually done…
Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro sequence, have some desirable features of pseudorandomness such as a large linear complexity and a small well-distribution measure. However, they also have some…
In this paper we study the action of the Binomial and Invert (interpolated) operators on the set of linear recurrent sequences. We prove that these operators preserve this set, and we determine how they change the characteristic…
Consider a finite irreducible Markov chain with invariant distribution $\pi$. We use the inner product induced by $\pi$ and the associated heat operator to simplify and generalize some results related to graph partitioning and the small-set…
We introduce an efficient method for deriving hierarchical constraints on the discontinuities of individual Feynman integrals. This method can be applied at any loop order and particle multiplicity, and to any configuration of massive or…
We study the problem of reconfiguring one minimum $s$-$t$-separator $A$ into another minimum $s$-$t$-separator $B$ in some $n$-vertex graph $G$ containing two non-adjacent vertices $s$ and $t$. We consider several variants of the problem as…
The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…
Ideally, the time that an incremental algorithm uses to process a change should be a function of the size of the change rather than, say, the size of the entire current input. Based on a formalization of ``the set of things changed'' by an…
A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…
Starting from an n-by-n matrix of zeros, choose uniformly random zero entries and change them to ones, one-at-a-time, until the matrix becomes invertible. We show that with probability tending to one as n tends to infinity, this occurs at…
An effective indexing scheme for clusters that enables fast structure comparison and congruence check is desperately desirable in the field of mathematics, artificial intelligence, materials science, etc. Here we introduce the concept of…
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia…
The construction of affine interval exchange maps with wandering intervals that are semi-conjugate with a given self-similar interval exchange map is strongly related with the existence of the so called minimal sequences associated with…