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COMBINATORICS

2006

2006

Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and there are at most s integers k, i < k < j, such that = [. . . j . . . k . . . i . . .]. In this short paper we determine the maximum number of edges in ,s for all s 1 and characterize all permutations which achieve this maximum. This answers an open question of Adin and Roichman, who studied the case s = 0. We also consider another (closely related) permutation graph, defined by Adin and Roichman, and obtain asymptotically tight bounds on the maximum number of edges in it.

Related Content

Added |
11 Dec 2010 |

Updated |
11 Dec 2010 |

Type |
Journal |

Year |
2006 |

Where |
COMBINATORICS |

Authors |
Peter Keevash, Po-Shen Loh, Benny Sudakov |

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