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A proof of the $m$-Symmetric Macdonald positivity at $t=1$ — arXiv:2608.10223

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.10223
License (as archived): CC0-1.0
Archived: 2026-10-19T06:27:22.753Z
SHA-256 of the archived text: d9991be3f7519a4f866b1ef87ae032f0da591bf93d11db166ba8ab7f889b3071
Stable URL of this page: https://metraipolis.com/documento/dc_fa02ecd7903d

How to cite

A proof of the $m$-Symmetric Macdonald positivity at $t=1$ — arXiv:2608.10223 — arXiv (en), https://arxiv.org/abs/2608.10223 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fa02ecd7903d (Metraipolis archive dc_fa02ecd7903d, sha256 d9991be3f7519a4f866b1ef87ae032f0da591bf93d11db166ba8ab7f889b3071)

BibTeX

@misc{dcfa02ecd7903d,
  title = {A proof of the $m$-Symmetric Macdonald positivity at $t=1$ — arXiv:2608.10223},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.10223},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fa02ecd7903d; sha256 d9991be3f7519a4f866b1ef87ae032f0da591bf93d11db166ba8ab7f889b3071},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.10223. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove, in the case $t=1$, the extension to the $m$-symmetric world of the original Macdonald positivity conjecture. This is achieved by giving a combinatorial interpretation of the Kostka coefficients $K_{\Omega \Lambda}(q,1)$ in terms of standard fillings of the diagram associated to the $m$-partition $\Omega$. This interpretation generalizes the one in the usual Macdonald case, which is given by a major index statistic on standard tableaux.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-12 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.10223 — 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 2026-10-19T06:20:30.682Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-12?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).