On multi-dimensional patterns

Sergey Kitaev, Jakayla Robbins

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)291-299
Number of pages9
JournalPure Mathematics and Applications
Issue number3-4
Publication statusPublished - 2007


  • pattern occurrence
  • permutations
  • bipartite graphs


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