Metric intersection problems in Cayley graphs and the Stirling recursion

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

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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
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 09 Oct 2013 01:25
Last Modified: 21 Apr 2020 21:58
URI: https://ueaeprints.uea.ac.uk/id/eprint/43639
DOI: 10.1007/s00010-013-0196-8

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