Maximum Size of Reverse-Free Sets of Permutations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10141895" target="_blank" >RIV/00216208:11320/13:10141895 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/120888168" target="_blank" >http://dx.doi.org/10.1137/120888168</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/120888168" target="_blank" >10.1137/120888168</a>

Result language
angličtina
Original language name
Maximum Size of Reverse-Free Sets of Permutations
Original language description
Two words have a reverse if they have the same pair of distinct letters on the same pair of positions, but in reversed order. A set of words no two of which have a reverse is said to be reverse-free. Let F(n, k) be the maximum size of a reverse-free setof words from [n]^k, where no letter repeats within a word. We show the following lower and upper bounds in the case n }= k: F(n, k) is of the order n^k k^(-k/2+O(k/log k)). As a consequence of the lower bound, a set of n-permutations, each two having areverse, has size at most n^(n/2+O(n/log n)).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GD201%2F09%2FH057" target="_blank" >GD201/09/H057: Res Informatica</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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