### Abstract

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

Article number | A34 |

Number of pages | 16 |

Journal | Integers: Electronic Journal of Combinatorial Number Theory |

Volume | 6 |

Publication status | Published - 11 Feb 2006 |

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### Keywords

- segmented patterns
- palindromic compositions
- bijections

### Cite this

*Integers: Electronic Journal of Combinatorial Number Theory*,

*6*, [A34].

}

*Integers: Electronic Journal of Combinatorial Number Theory*, vol. 6, A34.

**Enumerating segmented patterns in compositions and encoding with restricted permutations.** / Kitaev, Sergey; McAllister, Tyrrell; Petersen, T. Kyle.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Enumerating segmented patterns in compositions and encoding with restricted permutations

AU - Kitaev, Sergey

AU - McAllister, Tyrrell

AU - Petersen, T. Kyle

PY - 2006/2/11

Y1 - 2006/2/11

N2 - A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of occurrences of arbitrary segmented partially ordered patterns among compositions of n with a prescribed number of parts. These patterns generalize the notions of rises, drops, and levels studied in the literature. We also obtain results enumerating parts with given sizes and locations among compositions and palindromic compositions with a given number of parts. Our results are motivated by “encoding by restricted permutations,” a relatively undeveloped method that provides a language for describing many combinatorial objects. We conclude with some examples demonstrating bijections between restricted permutations and other objects.

AB - A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of occurrences of arbitrary segmented partially ordered patterns among compositions of n with a prescribed number of parts. These patterns generalize the notions of rises, drops, and levels studied in the literature. We also obtain results enumerating parts with given sizes and locations among compositions and palindromic compositions with a given number of parts. Our results are motivated by “encoding by restricted permutations,” a relatively undeveloped method that provides a language for describing many combinatorial objects. We conclude with some examples demonstrating bijections between restricted permutations and other objects.

KW - segmented patterns

KW - palindromic compositions

KW - bijections

UR - http://www.integers-ejcnt.org/vol6.html

M3 - Article

VL - 6

JO - Integers: Electronic Journal of Combinatorial Number Theory

JF - Integers: Electronic Journal of Combinatorial Number Theory

SN - 1553-1732

M1 - A34

ER -