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PreprintCC BY-NC-ND 4.0arXiv

Rational decomposition of polyhedra and a conjecture of Brlek and Reutenauer

  • Flavio D'Alessandro
  • Paolo Papi
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Abstract

We prove in the affirmative a conjecture of Brlek and Reutenauer (2003), which relates unambiguous rational sets to a well known result due to Khovanskii and Pukhlikov (1992) and independently to Lawrence (1990) on the valuations of the algebra spanned by the indicator functions of polyhedra.

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Cite

BibTeXRIS
BibTeX
@misc{dalessandro2026rational,
  title = {{Rational decomposition of polyhedra and a conjecture of Brlek and Reutenauer}},
  author = {Flavio D'Alessandro and Paolo Papi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22663},
  eprint = {2610.22663},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22663},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Rational decomposition of polyhedra and a conjecture of Brlek and Reutenauer
AU  - Flavio D'Alessandro
AU  - Paolo Papi
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22663
UR  - https://arxiv.org/abs/2610.22663
AB  - We prove in the affirmative a conjecture of Brlek and Reutenauer (2003), which relates unambiguous rational sets to a well known result due to Khovanskii and Pukhlikov (1992) and independently to Lawrence (1990) on the valuations of the algebra spanned by the indicator functions of polyhedra.
ER  -