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PreprintarXiv licencearXiv

Relative Dimension of Posets

  • Dominik Dürrschnabel
  • Jędrzej Hodor
  • Piotr Micek
  • Gerd Stumme
  • William T. Trotter
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Abstract

Dimension of partially ordered sets (posets for short) can be seen as a measure of how much space is needed to store posets. Refining the definition of dimension, or actually the local dimension, in this respect we obtain the notion of relative dimension. We discuss properties of relative dimension and we give bounds for relative dimension of some well-known families of posets.

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Cite

BibTeXRIS
BibTeX
@misc{durrschnabel2026relative,
  title = {{Relative Dimension of Posets}},
  author = {Dominik Dürrschnabel and Jędrzej Hodor and Piotr Micek and Gerd Stumme and William T. Trotter},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05166},
  eprint = {2609.05166},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05166},
}
RIS
TY  - UNPB
TI  - Relative Dimension of Posets
AU  - Dominik Dürrschnabel
AU  - Jędrzej Hodor
AU  - Piotr Micek
AU  - Gerd Stumme
AU  - William T. Trotter
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05166
UR  - https://arxiv.org/abs/2609.05166
AB  - Dimension of partially ordered sets (posets for short) can be seen as a measure of how much space is needed to store posets. Refining the definition of dimension, or actually the local dimension, in this respect we obtain the notion of relative dimension. We discuss properties of relative dimension and we give bounds for relative dimension of some well-known families of posets.
ER  -