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Forests of label-increasing trees

✍ Scribed by John Riordan

Publisher: John Wiley and Sons
Year: 1979
Tongue: English
Weight: 210 KB
Volume: 3
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190030204

No coin nor oath required. For personal study only.

✦ Synopsis

Label-increasing trees are fully labeled rooted trees with the restriction that the labels are in increasing order on every path from the root; the best known example is the binary case-no tree with more than two branches at the root, or internal vertices of degree greater than threeextensively examined by Foata and Schutzenberger in A Survey of Combinatorial Theory. The forests without branching restrictions are enumerated by number of trees by F , ( x ) = x ( x + l ) ~~~( x + n -l ) .

n > l (F,(x)=l), whose equivalent: F,(x)=Y,,(xT,, .. . , x T , ) , F,,(l)=T,,,=n!, is readily adapted to branching restriction.

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