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PreprintCC BY 4.0arXiv

Some sequences and number triangles which are related to Narayana polynomials and to q-Narayana polynomials for q=-1

  • Johann Cigler
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Abstract

As is well known the Catalan numbers can be interpreted as numbers of Dyck paths. The Narayana polynomials and the q-Narayana polynomials for q=-1 can analogously be interpreted as certain weights of these paths. In the present note we try to get some information about the corresponding weights of bounded Dyck paths. This also leads to some number sequences and analogues of Pascals triangle which previously have occurred in other contexts. We consider some examples and obtain some results and conjectures.

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Cite

BibTeXRIS
BibTeX
@misc{cigler2026some,
  title = {{Some sequences and number triangles which are related to Narayana polynomials and to q-Narayana polynomials for q=-1}},
  author = {Johann Cigler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.03363},
  eprint = {2608.03363},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.03363},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Some sequences and number triangles which are related to Narayana polynomials and to q-Narayana polynomials for q=-1
AU  - Johann Cigler
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2608.03363
UR  - https://arxiv.org/abs/2608.03363
AB  - As is well known the Catalan numbers can be interpreted as numbers of Dyck paths. The Narayana polynomials and the q-Narayana polynomials for q=-1 can analogously be interpreted as certain weights of these paths. In the present note we try to get some information about the corresponding weights of bounded Dyck paths. This also leads to some number sequences and analogues of Pascals triangle which previously have occurred in other contexts. We consider some examples and obtain some results and conjectures.
ER  -