arXiv Open Access 2025

Falling stars: a fall-decorated rational shuffle theorem

Alessandro Iraci Roberto Pagaria Giovanni Paolini

Lihat Sumber

Abstrak

In this paper, we formulate a rational analog of the fall Delta theorem and the Delta square conjecture. We find a new dinv statistic on fall-decorated paths on a $(m+k) \times (n+k)$ rectangle that simultaneously extends the previously known dinv statistics on decorated square objects and non-decorated rectangular objects. We prove a symmetric function formula for the $q,t$-generating function of fall-decorated rectangular Dyck paths as a skewing operator applied to $e_{m,n+km}$ and, conditionally on the rectangular paths conjecture, an analog formula for fall-decorated rectangular paths.

Topik & Kata Kunci

math.CO

Penulis (3)

Alessandro Iraci

Roberto Pagaria

Giovanni Paolini

Format Sitasi

APA MLA BibTeX

Iraci, A., Pagaria, R., Paolini, G. (2025). Falling stars: a fall-decorated rational shuffle theorem. https://arxiv.org/abs/2508.20935

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓