Talonnumero

Talonnumero is a conceptual labeling scheme used in theoretical discussions of hierarchical tagging systems and is not a standard deployed in production environments. In this context, a talon represents a node in a rooted tree, such as a taxonomy, directory, or facet structure. The term blends talon and numero (number) to emphasize numeric labeling of talons.

Definition: Given a finite rooted tree T with root r, talonnumero assigns to each node t a unique positive integer f(t) via a depth-first pre-order traversal, starting at 1. The resulting labels provide a compact linearization of the hierarchy.

Properties: The labeling is unique for each node and order-preserving with respect to the traversal. For any node t with subtree S, the set {f(u) : u in S} forms a consecutive interval [f(t), f(t) + |S| - 1]. Because the intervals depend on the tree structure, changes to the hierarchy may require remapping, so talonnumero is typically used as a snapshot labeling rather than a dynamic scheme.

Variants: The standard form uses depth-first pre-order numbering; breadth-first (level-order) numbering is a common variant that yields different interval properties. Some adaptations append suffixes or pair the base number with auxiliary data to encode sibling order without altering the core pre-order values.

Applications: Talonnumero is used in theoretical models of data organization, archival indexing, and search algorithms where subtree queries benefit from a linear interval representation. It also serves as an educational example for illustrating tree labeling and hierarchical numbering.

History: The concept emerged in computer science education as a didactic tool for explaining how hierarchical structures can be serialized into a linear label space. It remains a conceptual construct rather than a widely adopted standard.

See also: preorder traversal, tree labeling, hierarchical numbering, indexing, taxonomy.