### Abstract

Original language | English |
---|---|

Pages (from-to) | 291-299 |

Number of pages | 9 |

Journal | Pure Mathematics and Applications |

Volume | 18 |

Issue number | 3-4 |

Publication status | Published - 2007 |

### Fingerprint

### Keywords

- pattern occurrence
- permutations
- bipartite graphs

### Cite this

*Pure Mathematics and Applications*,

*18*(3-4), 291-299.

}

*Pure Mathematics and Applications*, vol. 18, no. 3-4, pp. 291-299.

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

Research output: Contribution to journal › Article

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

JF - Pure Mathematics and Applications

SN - 1218-4586

IS - 3-4

ER -