PreprintCC BY 4.0Zenodo
An explicit positive formula for the sorting difference in Lam–Pylyavskyy Conjecture 53
Abstract
This paper proves Lam–Pylyavskyy Conjecture 53 on Schur Q-positivity under sorting of strict partitions. We give an explicit expansion of the sorting difference as a nonnegative integer combination of images of ordinary Schur functions under the homomorphism that annihilates even power sums and doubles odd power sums. The proof combines a signed Pfaffian–minor identity with the hook formula and Frobenius Giambelli identity. Common parts are handled by block elimination, while a padding rule treats odd lengths. The formula also implies that every Schur Q-coefficient is divisible by 2k+1, where k is the number of common parts.
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BibTeX
@misc{chen2026explicit,
title = {{An explicit positive formula for the sorting difference in Lam–Pylyavskyy Conjecture 53}},
author = {Sihan Chen},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23573807},
url = {https://zenodo.org/records/23573807},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An explicit positive formula for the sorting difference in Lam–Pylyavskyy Conjecture 53
AU - Sihan Chen
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23573807
UR - https://zenodo.org/records/23573807
AB - This paper proves Lam–Pylyavskyy Conjecture 53 on Schur Q-positivity under sorting of strict partitions. We give an explicit expansion of the sorting difference as a nonnegative integer combination of images of ordinary Schur functions under the homomorphism that annihilates even power sums and doubles odd power sums. The proof combines a signed Pfaffian–minor identity with the hook formula and Frobenius Giambelli identity. Common parts are handled by block elimination, while a padding rule treats odd lengths. The formula also implies that every Schur Q-coefficient is divisible by 2^k+1, where k is the number of common parts.
ER -