<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al. to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amsil-2022-0015_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mfrac><mn>5</mn><mn>3</mn></mfrac></mrow></math>
<tex-math>{5 \over 3}</tex-math>
</alternatives>
</inline-formula> when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches 2.</p>
</abstract>

A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al. to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches 


53
{5 \over 3}

 when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches 2.

Deepest Nodes in Marked Ordered Trees

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Deepest Nodes in Marked Ordered Trees"}

A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees...

Deepest Nodes in Marked Ordered Trees

Published Online: Sep 08, 2022

Page range: 215 - 227

Received: Feb 17, 2022

Accepted: Aug 16, 2022

DOI: https://doi.org/10.2478/amsil-2022-0015

Keywords
marked ordered trees, skew Dyck paths, generating functions

© 2022 Helmut Prodinger, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Deepest Nodes in Marked Ordered Trees

Published Online: Sep 08, 2022

Page range: 215 - 227

Received: Feb 17, 2022

Accepted: Aug 16, 2022

DOI: https://doi.org/10.2478/amsil-2022-0015

Keywordsmarked ordered trees, skew Dyck paths, generating functions

© 2022 Helmut Prodinger, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
marked ordered trees, skew Dyck paths, generating functions