# Decomposing labeled interval orders as pairs of permutations

Anders Claesson, Stuart Alexander Hannah

Research output: Contribution to journalArticle

### Abstract

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.
Original language English P4.16 20 The Electronic Journal of Combinatorics 21 4 Published - 16 Oct 2014

### Fingerprint

Interval Order
Permutation
Involution
Ascent
Signed
Bijection
Enumeration
Generating Function
Table
Inversion
Classify
Decompose

### Keywords

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

### Cite this

Claesson, Anders ; Hannah, Stuart Alexander. / Decomposing labeled interval orders as pairs of permutations. In: The Electronic Journal of Combinatorics. 2014 ; Vol. 21, No. 4.
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Decomposing labeled interval orders as pairs of permutations. / Claesson, Anders; Hannah, Stuart Alexander.

In: The Electronic Journal of Combinatorics, Vol. 21, No. 4, P4.16, 16.10.2014.

Research output: Contribution to journalArticle

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