### Abstract

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

Article number | P4.16 |

Number of pages | 20 |

Journal | The Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 4 |

Publication status | Published - 16 Oct 2014 |

### Fingerprint

### Keywords

- ballot matrix
- composition matrix
- sign reversing involution
- interval order
- 2+2-free posset
- ascent bottom

### Cite this

*The Electronic Journal of Combinatorics*,

*21*(4), [P4.16].

}

*The Electronic Journal of Combinatorics*, vol. 21, no. 4, P4.16.

**Decomposing labeled interval orders as pairs of permutations.** / Claesson, Anders; Hannah, Stuart Alexander.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Decomposing labeled interval orders as pairs of permutations

AU - Claesson, Anders

AU - Hannah, Stuart Alexander

PY - 2014/10/16

Y1 - 2014/10/16

N2 - We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices fixed under this involution are in bijection with labeled interval orders and that they decompose to a pair consisting of a permutation and an inversion table. To fully classify such pairs, results pertaining to the enumeration of permutations having a given set of ascent bottoms are given. This allows for a new formula for the number of labeled interval orders.

AB - We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices fixed under this involution are in bijection with labeled interval orders and that they decompose to a pair consisting of a permutation and an inversion table. To fully classify such pairs, results pertaining to the enumeration of permutations having a given set of ascent bottoms are given. This allows for a new formula for the number of labeled interval orders.

KW - ballot matrix

KW - composition matrix

KW - sign reversing involution

KW - interval order

KW - 2+2-free posset

KW - ascent bottom

UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i4p16

M3 - Article

VL - 21

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 4

M1 - P4.16

ER -