Phongpattanacharoen, Teeraphong and Siemons, Johannes
(2013)
*Metric intersection problems in Cayley graphs and the Stirling recursion.*
Aequationes Mathematicae, 85 (3).
pp. 387-408.
ISSN 0001-9054

## Abstract

In Sym(n) with n = 5 let H be a conjugacy class of elements of order 2 and let G be the Cayley graph whose vertex set is the group G generated by H (so G = Sym(n) or Alt(n)) and whose edge set is determined by H. We are interested in the metric structure of this graph. In particular, for g?G let B r (g) be the metric ball in G of radius r and centre g. We show that the intersection numbers F(G;r,g):=|Br(e)nBr(g)| are generalized Stirling functions in n and r. The results are motivated by the study of error graphs in Levenshtein (Dokl Akad Nauk 354:593–596, 1997; IEEE Trans Inform Theory 47(1):2–22, 2001; (J Comb Theory Ser A 93(2):310–332, 2001) and related reconstruction problems.

Item Type: | Article |
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Faculty \ School: | Faculty of Science > School of Mathematics |

Depositing User: | Pure Connector |

Date Deposited: | 09 Oct 2013 01:25 |

Last Modified: | 24 Oct 2022 04:45 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/43639 |

DOI: | 10.1007/s00010-013-0196-8 |

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