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A Koteljanskii inequality for permanents
Abstract
We prove a permanental analogue of Koteljanskii's inequality. If A is an inverse M-matrix that becomes symmetric after a positive diagonal similarity, then per(AS∪ T) per(AS∩ T)≥per(AS) per(AT) for all S,T⊆[n], where AS is the principal submatrix indexed by S. The proof expresses permanents as moments of a complex Gaussian vector and uses Ginibre's correlation inequality. Finally, an explicit counterexample shows that symmetry cannot be dropped.
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BibTeX
@misc{sra2026koteljanskii,
title = {{A Koteljanskii inequality for permanents}},
author = {Suvrit Sra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39979},
eprint = {2609.39979},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39979},
}
RIS
TY - UNPB
TI - A Koteljanskii inequality for permanents
AU - Suvrit Sra
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39979
UR - https://arxiv.org/abs/2609.39979
AB - We prove a permanental analogue of Koteljanskii's inequality. If A is an inverse M-matrix that becomes symmetric after a positive diagonal similarity, then per(A_S∪ T) per(A_S∩ T)≥per(A_S) per(A_T) for all S,T⊆[n], where A_S is the principal submatrix indexed by S. The proof expresses permanents as moments of a complex Gaussian vector and uses Ginibre's correlation inequality. Finally, an explicit counterexample shows that symmetry cannot be dropped.
ER -