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Chromatic word-quasisymmetric functions of matroids — arXiv:2609.29927

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.29927
License (as archived): CC0-1.0
Archived: 2026-10-08T06:41:00.979Z
SHA-256 of the archived text: c7b9b1790dd38f8d83e541917c9d0c099e19c88d7cd0434972c54e027e17dd2a
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How to cite

Chromatic word-quasisymmetric functions of matroids — arXiv:2609.29927 — arXiv (en), https://arxiv.org/abs/2609.29927 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_aaa4d39f36fb (Metraipolis archive dc_aaa4d39f36fb, sha256 c7b9b1790dd38f8d83e541917c9d0c099e19c88d7cd0434972c54e027e17dd2a)

BibTeX

@misc{dcaaa4d39f36fb,
  title = {Chromatic word-quasisymmetric functions of matroids — arXiv:2609.29927},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.29927},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_aaa4d39f36fb; sha256 c7b9b1790dd38f8d83e541917c9d0c099e19c88d7cd0434972c54e027e17dd2a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.29927. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Billera, Jia, and Reiner (2009) introduced the quasisymmetric functions of matroids and showed that this defines a Hopf algebra homomorphism which is a valuative invariant, i.e., isomorphic matroids have the same quasisymmetric function and polytopal subdivisions of matroid base polytopes define relations among the corresponding quasisymmetric functions. In this project we study an analogue in non-commuting variables, the word-quasisymmetric functions. To every matroid $M$ we associate a word-quasisymmetric function $\psi(M)$ and call this the chromatic word-quasisymmetric functions of a matroid. Matroids and word-quasisymmetric functions form Hopf algebras, and our map $\psi$ between them is a homomorphism. We want to study the kernel, equivalently the image, of the map $\psi$ from matroids to word-quasisymmetric functions, that is, we would like to understand which matroids are indistinguishable by the chromatic word-quasisymmetric functions. The map $\psi$ is not an invariant, but we can show that it is valuative. Using Schubert matroids and nested matroids, special classes of matroids, we prove a lower bound of $2^d-d$ for the rank of the map $\psi$ from matroids to the chromatic word-quasisymmetric functions in degree $d$ and conjecture the upper bound of $d!$ is tight.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.29927 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T06:02:10.078Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).