Skip to content
DraconiticResearch
Search Sources API
201,642 studies31 sourcesUpdated 14 min ago
PreprintCC BY 4.0arXiv

Types of well-founded trees and the homomorphism order

  • Jakub Smolík
Open at sourcePDFDOICite

Abstract

We introduce an ordinal-valued invariant of well-founded trees, called their type. We use type to give an alternative proof that the class of all well-founded trees is well-quasi-ordered by the homomorphism relation, and we establish a relationship between type and the usual ordinal rank of a well-founded tree, showing in particular that type provides a strictly coarser structural classification.

Related

  1. Maximal Order Type and Width of the h-Preorder on Finite Labeled Trees
    Ilya Smirnov
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsLogic & foundationsarXiv
  2. The order types of the supports of p-adic algebraic Hahn series
    Shanwen Wang, Yijun Yuan
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Blow-ups of order types of positive density
    Ruy Fabila-Monroy, Benedikt Hahn, Jesús Leaños
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  4. The Number of Tropical Order Types and Coherent Matching Fields
    Xavier Allamigeon, Yiyuan Chen, Stéphane Gaubert +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. Well-balanced second-order approximation of the compressible atmospheric Euler equations
    Crystal Farris, Matthias Maier, Eric J. Tovar
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{smolik2026types,
  title = {{Types of well-founded trees and the homomorphism order}},
  author = {Jakub Smolík},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.02136},
  eprint = {2608.02136},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.02136},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Types of well-founded trees and the homomorphism order
AU  - Jakub Smolík
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2608.02136
UR  - https://arxiv.org/abs/2608.02136
AB  - We introduce an ordinal-valued invariant of well-founded trees, called their type. We use type to give an alternative proof that the class of all well-founded trees is well-quasi-ordered by the homomorphism relation, and we establish a relationship between type and the usual ordinal rank of a well-founded tree, showing in particular that type provides a strictly coarser structural classification.
ER  -