What question did this study set out to answer?

The aim is to demonstrate that almost all trees contain a fixed finite tree as a subtree and to explore the implications for automorphism groups.

June 29, 2026Archiv der MathematikOpen Access

Patterns in trees and quantum automorphism groups

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The aim is to demonstrate that almost all trees contain a fixed finite tree as a subtree and to explore the implications for automorphism groups.
Proving the inclusion of a fixed finite tree as a subtree in almost all trees.
Demonstrating how this inclusion induces an embedding of the corresponding (quantum) automorphism groups.
Almost all trees contain a fixed finite tree as a subtree.
The inclusion induces an embedding of the corresponding automorphism groups, revealing generic properties.

Implication

This research proves that most trees contain fixed finite trees as subtrees, suggesting new properties of automorphism groups.

Abstract

We prove that given a fixed finite tree P , almost all trees contain P as a subtree. Moreover, the inclusion can be made so that it induces an embedding of the corresponding (quantum) automorphism groups, thereby providing generic properties of the latter.

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Cite This Study

Alger et al. (2026) studied this question.

synapsesocial.com/papers/6a420a74f91bb43ea9191c5c https://doi.org/10.1007/s00013-026-02260-z

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Implication

This research proves that most trees contain fixed finite trees as subtrees, suggesting new properties of automorphism groups.

Patterns in trees and quantum automorphism groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Patterns in trees and quantum automorphism groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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