# interleave sequence

Let $S$ be a set, and let $\{{x}_{i}\},i=0,1,2,\mathrm{\dots}$ and $\{{y}_{i}\},i=0,1,2,\mathrm{\dots}$ be two sequences^{} in $S$. The interleave sequence is defined to be the sequence ${x}_{0},{y}_{0},{x}_{1},{y}_{1},\mathrm{\dots}$. Formally, it is the sequence $\{{z}_{i}\},i=0,1,2,\mathrm{\dots}$ given by

$${z}_{i}:=\{\begin{array}{cc}{x}_{k}\hfill & \text{if}i=2k\text{is even,}\hfill \\ {y}_{k}\hfill & \text{if}i=2k+1\text{is odd.}\hfill \end{array}$$ |

Title | interleave sequence |
---|---|

Canonical name | InterleaveSequence |

Date of creation | 2013-03-22 11:52:12 |

Last modified on | 2013-03-22 11:52:12 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 7 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 26A03 |

Classification | msc 40-00 |

Classification | msc 11A15 |