Related papers: Large Sets Avoiding Rough Patterns

There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to…

This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.

Ascent sequences form a central class of combinatorial objects, as they are in bijection with several important families such as (2+2)-free posets, Stoimenow matchings, and other Fishburn objects, and are enumerated by the Fishburn numbers.…

In this thesis, we consider the problem of characterizing and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment. We are interested in a well known subclass of…

Fix a strong rectangulation pattern $P$ of size $L$. We show that the growth constant of the class of strong rectangulations avoiding $P$ is strictly smaller than $\Lambda =27/2$, the growth constant for all strong rectangulations. More…

We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices…

We study the longest increasing subsequence problem for random permutations avoiding the pattern $312$ and another pattern $\tau$ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average…

We introduce a notion of pattern occurrence that generalizes both classical permutation patterns as well as poset containment. Many questions about pattern statistics and avoidance generalize naturally to this setting, and we focus on…

We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…

Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap…

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…

An infinte word w avoids a pattern p with the involution t if there is no substitution for the variables in p and no involution t such that the resulting word is a factor of w. We investigate the avoidance of patterns with respect to the…

This paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional mesh patterns of length 1. A pattern is avoidable if there…

The study of patterns in permutations in a very active area of current research. Klazar defined and studied an analogous notion of pattern for set partitions. We continue this work, finding exact formulas for the number of set partitions…

We present four constructions of inversion sequences, and use them to compute the enumeration sequences of 24 classes of pattern-avoiding inversion sequences. This completes the enumeration of inversion sequences avoiding one or two…

We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…

In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for avoiding the permutation 12. We also give exact enumeration for ordered partitions with…

Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some…

We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf…

Upper bounds to the size of a family of subsets of an n-element set that avoids certain configurations are proved. These forbidden configurations can be described by inclusion patterns and some sets having the same size. Our results are…