Schur positivity of three-legged spiders

@misc{wang2026schur,
  title = {{Schur positivity of three-legged spiders}},
  author = {David G. L. Wang and Watson Z. Y. Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03464},
  eprint = {2610.03464},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03464},
}

TY  - UNPB
TI  - Schur positivity of three-legged spiders
AU  - David G. L. Wang
AU  - Watson Z. Y. Wang
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03464
UR  - https://arxiv.org/abs/2610.03464
AB  - We give a complete classification of Schur positivity for three-legged spiders. Every spider with at least two even legs is Schur positive, whereas every spider with three odd legs has a negative Schur coefficient. If a is even and b,c are odd, then the spider S(a,b,c) is Schur positive if and only if a≤ 5b+5c+2. Whenever Schur positivity fails, there is exactly one negative Schur coefficient, whose value we determine explicitly. These results extend those of Thibon and Wang for the families S(a,2,1) and S(a,4,1), and those of Wang and Wang for S(a,b,2). The proof combines known Schur-positivity results for clique-spiders with Pieri's rule and simultaneous induction.
ER  -