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PreprintCC BY 4.0arXiv

Two families of Young tableaux with periodic walls: Counting formulas and differential transcendence

  • Feihu Liu
  • Jiahang Liu
  • Guoce Xin
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Abstract

Banderier, Marchal, and Wallner studied the enumeration problem for Young tableaux with walls. These are similar to standard Young tableaux, except that local decreases are allowed at some walls. In 2021, Banderier and Wallner counted Young tableaux with periodic walls, in which the elementary blocks are Young diagrams of shape (2,2). They obtained exact counting formulas for $30$ of the $32$ classes up to symmetry. In this paper, we first derive recurrences for counting the remaining two classes of Young tableaux with periodic walls. We then prove that their counting exponential generating functions are differentially transcendental. Consequently, they are neither D-algebraic nor D-finite. This disproves a conjecture of Banderier and Wallner.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026families,
  title = {{Two families of Young tableaux with periodic walls: Counting formulas and differential transcendence}},
  author = {Feihu Liu and Jiahang Liu and Guoce Xin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35067},
  eprint = {2610.35067},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35067},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Two families of Young tableaux with periodic walls: Counting formulas and differential transcendence
AU  - Feihu Liu
AU  - Jiahang Liu
AU  - Guoce Xin
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.35067
UR  - https://arxiv.org/abs/2610.35067
AB  - Banderier, Marchal, and Wallner studied the enumeration problem for Young tableaux with walls. These are similar to standard Young tableaux, except that local decreases are allowed at some walls. In 2021, Banderier and Wallner counted Young tableaux with periodic walls, in which the elementary blocks are Young diagrams of shape (2,2). They obtained exact counting formulas for $30$ of the $32$ classes up to symmetry. In this paper, we first derive recurrences for counting the remaining two classes of Young tableaux with periodic walls. We then prove that their counting exponential generating functions are differentially transcendental. Consequently, they are neither D-algebraic nor D-finite. This disproves a conjecture of Banderier and Wallner.
ER  -