On multi-dimensional patterns

Sergey Kitaev, Jakayla Robbins

Research output: Contribution to journalArticle

Abstract

We generalize the concept of pattern occurrence in permutations, words or matrices to that in n-dimensional objects, which are basically sets of (n + 1)-tuples. In the case n = 3, we give a possible interpretation of such patterns in terms of bipartite graphs. For zero-box patterns we study vanishing borders related to bipartite Ramsey problems in the case of two dimensions. Also, we study the maximal number of 1’s in binary objects avoiding (in two different senses) a zero-box pattern.
LanguageEnglish
Pages291-299
Number of pages9
JournalPure Mathematics and Applications
Volume18
Issue number3-4
Publication statusPublished - 2007

Fingerprint

Zero
Bipartite Graph
n-dimensional
Two Dimensions
Permutation
Binary
Generalise
Object
Interpretation
Concepts

Keywords

  • pattern occurrence
  • permutations
  • bipartite graphs

Cite this

Kitaev, Sergey ; Robbins, Jakayla. / On multi-dimensional patterns. In: Pure Mathematics and Applications. 2007 ; Vol. 18, No. 3-4. pp. 291-299.
@article{152945d534ae4590ab3b5b71ad7b4d85,
title = "On multi-dimensional patterns",
abstract = "We generalize the concept of pattern occurrence in permutations, words or matrices to that in n-dimensional objects, which are basically sets of (n + 1)-tuples. In the case n = 3, we give a possible interpretation of such patterns in terms of bipartite graphs. For zero-box patterns we study vanishing borders related to bipartite Ramsey problems in the case of two dimensions. Also, we study the maximal number of 1’s in binary objects avoiding (in two different senses) a zero-box pattern.",
keywords = "pattern occurrence, permutations, bipartite graphs",
author = "Sergey Kitaev and Jakayla Robbins",
year = "2007",
language = "English",
volume = "18",
pages = "291--299",
journal = "Pure Mathematics and Applications",
issn = "1218-4586",
number = "3-4",

}

Kitaev, S & Robbins, J 2007, 'On multi-dimensional patterns' Pure Mathematics and Applications, vol. 18, no. 3-4, pp. 291-299.

On multi-dimensional patterns. / Kitaev, Sergey; Robbins, Jakayla.

In: Pure Mathematics and Applications, Vol. 18, No. 3-4, 2007, p. 291-299.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On multi-dimensional patterns

AU - Kitaev, Sergey

AU - Robbins, Jakayla

PY - 2007

Y1 - 2007

N2 - We generalize the concept of pattern occurrence in permutations, words or matrices to that in n-dimensional objects, which are basically sets of (n + 1)-tuples. In the case n = 3, we give a possible interpretation of such patterns in terms of bipartite graphs. For zero-box patterns we study vanishing borders related to bipartite Ramsey problems in the case of two dimensions. Also, we study the maximal number of 1’s in binary objects avoiding (in two different senses) a zero-box pattern.

AB - We generalize the concept of pattern occurrence in permutations, words or matrices to that in n-dimensional objects, which are basically sets of (n + 1)-tuples. In the case n = 3, we give a possible interpretation of such patterns in terms of bipartite graphs. For zero-box patterns we study vanishing borders related to bipartite Ramsey problems in the case of two dimensions. Also, we study the maximal number of 1’s in binary objects avoiding (in two different senses) a zero-box pattern.

KW - pattern occurrence

KW - permutations

KW - bipartite graphs

UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/multi-dim-patterns.pdf

UR - http://puma.dimai.unifi.it/18_3_4.php

M3 - Article

VL - 18

SP - 291

EP - 299

JO - Pure Mathematics and Applications

T2 - Pure Mathematics and Applications

JF - Pure Mathematics and Applications

SN - 1218-4586

IS - 3-4

ER -