Local extrema in random trees
The number of local maxima (resp., local minima) in a tree T∈𝒯n rooted at r∈[n] is denoted by Mr(T) (resp., by mr(T)). We find exact formulas as rational functions of n for the expectation and variance of M1(T) and mn(T) when T∈𝒯n is chosen randomly according to a uniform distribution. As a conseque...
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| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3867 |
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| _version_ | 1832563543099047936 |
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| author | Lane Clark |
| author_facet | Lane Clark |
| author_sort | Lane Clark |
| collection | DOAJ |
| description | The number of local maxima (resp., local minima) in a tree T∈𝒯n rooted at r∈[n] is denoted by Mr(T) (resp., by mr(T)). We find exact formulas as rational functions of n for the expectation and
variance of M1(T) and mn(T) when T∈𝒯n is chosen
randomly according to a uniform distribution. As a consequence,
a.a.s. M1(T) and mn(T) belong to a relatively small interval
when T∈𝒯n. |
| format | Article |
| id | doaj-art-166b426548f74bf584de16bf2524018b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-166b426548f74bf584de16bf2524018b2025-02-03T01:13:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005233867388210.1155/IJMMS.2005.3867Local extrema in random treesLane Clark0Department of Mathematics, College of Science, Southern Illinois University Carbondale, Carbondale 62901-4408, IL, USAThe number of local maxima (resp., local minima) in a tree T∈𝒯n rooted at r∈[n] is denoted by Mr(T) (resp., by mr(T)). We find exact formulas as rational functions of n for the expectation and variance of M1(T) and mn(T) when T∈𝒯n is chosen randomly according to a uniform distribution. As a consequence, a.a.s. M1(T) and mn(T) belong to a relatively small interval when T∈𝒯n.http://dx.doi.org/10.1155/IJMMS.2005.3867 |
| spellingShingle | Lane Clark Local extrema in random trees International Journal of Mathematics and Mathematical Sciences |
| title | Local extrema in random trees |
| title_full | Local extrema in random trees |
| title_fullStr | Local extrema in random trees |
| title_full_unstemmed | Local extrema in random trees |
| title_short | Local extrema in random trees |
| title_sort | local extrema in random trees |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3867 |
| work_keys_str_mv | AT laneclark localextremainrandomtrees |