Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Combinatorics

arXiv:2202.06153 (math)
[Submitted on 12 Feb 2022 (v1), last revised 18 Jul 2023 (this version, v3)]

Title:A $q$-deformation of enriched $P$-partitions (extended abstract)

Authors:Darij Grinberg, Ekaterina A. Vassilieva
View PDF
Abstract:We introduce a $q$-deformation that generalises in a single framework previous works on classical and enriched $P$-partitions. In particular, we build a new family of power series with a parameter $q$ that interpolates between Gessel's fundamental ($q=0$) and Stembridge's peak quasisymmetric functions ($q=1$) and show that it is a basis of $\QSym$ when $q\notin\{-1,1\}$. Furthermore we build their corresponding monomial bases parametrised with $q$ that cover our previous work on enriched monomials and the essential quasisymmetric functions of Hoffman.
Comments: 12 pages. Extended abstract accepted for FPSAC 2022. In v3, we corrected Corollary 1
Subjects: Combinatorics (math.CO)
MSC classes: 05E05, 06A11
Cite as: arXiv:2202.06153 [math.CO]
  (or arXiv:2202.06153v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2202.06153
Journal reference: corrected version of: Séminaire Lotharingien de Combinatoire, 86B.78 (2022), 12 pp

Submission history

From: Darij Grinberg [view email]
[v1] Sat, 12 Feb 2022 21:56:58 UTC (18 KB)
[v2] Sun, 3 Apr 2022 22:38:56 UTC (20 KB)
[v3] Tue, 18 Jul 2023 17:46:10 UTC (20 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
license icon view license
Current browse context:
math.CO
< prev   |   next >
new | recent | 2022-02
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)