### Abstract

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

Pages (from-to) | 159-173 |

Number of pages | 15 |

Journal | Australasian Journal of Combinatorics |

Volume | 48 |

Publication status | Published - Oct 2010 |

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### Keywords

- Ferrers graph
- boolean complex
- bipartite graphs

### Cite this

*Australasian Journal of Combinatorics*,

*48*, 159-173.

}

*Australasian Journal of Combinatorics*, vol. 48, pp. 159-173.

**Boolean complexes for Ferrers graphs.** / Claesson, Anders; Kitaev, Sergey; Ragnarsson, Kari; Tenner, Bridget Eileen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Boolean complexes for Ferrers graphs

AU - Claesson, Anders

AU - Kitaev, Sergey

AU - Ragnarsson, Kari

AU - Tenner, Bridget Eileen

PY - 2010/10

Y1 - 2010/10

N2 - In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show that the boolean numbers of the associated Ferrers graphs are the Genocchi numbers of the second kind, and obtain a relation between the Legendre-Stirling numbers and the Genocchi numbers of the second kind. In another application, we compute the boolean number of a complete bipartite graph, corresponding to a rectangular Ferrers shape, which is expressed in terms of the Stirling numbers of the second kind. Finally, we analyze the complexity of calculating the boolean number of a Ferrers graph using these results and show that it is a significant improvement over calculating by edge recursion.

AB - In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show that the boolean numbers of the associated Ferrers graphs are the Genocchi numbers of the second kind, and obtain a relation between the Legendre-Stirling numbers and the Genocchi numbers of the second kind. In another application, we compute the boolean number of a complete bipartite graph, corresponding to a rectangular Ferrers shape, which is expressed in terms of the Stirling numbers of the second kind. Finally, we analyze the complexity of calculating the boolean number of a Ferrers graph using these results and show that it is a significant improvement over calculating by edge recursion.

KW - Ferrers graph

KW - boolean complex

KW - bipartite graphs

UR - http://ajc.maths.uq.edu.au/?page=get_volumes&volume=48

UR - http://arxiv.org/abs/0808.2307

M3 - Article

VL - 48

SP - 159

EP - 173

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

ER -