Related papers: The computational landscape of permutation pattern…
We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical…
Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…
Permutation Pattern Matching (PPM) is the problem of deciding for a given pair of permutations P and T whether the pattern P is contained in the text T. Bose, Buss and Lubiw showed that PPM is NP-complete. In view of this result, it is…
Any permutation statistic $f:\sym\to\CC$ may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: $f= \Sigma_\tau\lambda_f(\tau)\tau$. To provide explicit expansions for certain…
Recent advances in learning-based image compression typically come at the cost of high complexity. Designing computationally efficient architectures remains an open challenge. In this paper, we empirically investigate the impact of…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…
Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…
In statistical setting of the pattern recognition problem the number of examples required to approximate an unknown labelling function is linear in the VC dimension of the target learning class. In this work we consider the question whether…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$,…
Permutation is the different arrangements that can be made with a given number of things taking some or all of them at a time. The notation P(n,r) is used to denote the number of permutations of n things taken r at a time. Permutation is…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations $\pi$ and $\tau$, represented as sequences of integers, and the task is to determine whether $\tau$ contains a subsequence order-isomorphic to…
This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects not covered in the recent book by Kitaev, \emph{Patterns in Permutations and words}. I first survey recent developments on the enumeration…
One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial features of their environment, and use that information to compute the…
This is a survey primarily about determining the border rank of tensors, especially those relevant for the study of the complexity of matrix multiplication. This is a subject that on the one hand is of great significance in theoretical…
We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that…