A new pattern-enumeration formula for ordered trees that includes nonleaf-only pattern components is proven and used to count protected and unprotected nodes, stumps, and related tree families.
1700 Forests
1 Pith paper cite this work. Polarity classification is still indexing.
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Pith paper citing it
abstract
Since ordered trees and Dyck paths are equinumerous, so are ordered forests and grand-Dyck paths that start with an upwards step.
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cs.DM 1years
2019 1verdicts
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Nonleaf Patterns in Trees: Protected Nodes and Fine Numbers
A new pattern-enumeration formula for ordered trees that includes nonleaf-only pattern components is proven and used to count protected and unprotected nodes, stumps, and related tree families.