A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions
Forum of Mathematics, Sigma, Tome 12 (2024)
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We characterize totally symmetric self-complementary plane partitions (TSSCPP) as bounded compatible sequences satisfying a Yamanouchi-like condition. As such, they are in bijection with certain pipe dreams. Using this characterization and the recent bijection of Gao–Huang between reduced pipe dreams and reduced bumpless pipe dreams, we give a bijection between alternating sign matrices and TSSCPP in the reduced, 1432-avoiding case. We also give a different bijection in the 1432- and 2143-avoiding case that preserves natural poset structures on the associated pipe dreams and bumpless pipe dreams.
@article{10_1017_fms_2023_131,
author = {Daoji Huang and Jessica Striker},
title = {A {Pipe} {Dream} {Perspective} on {Totally} {Symmetric} {Self-Complementary} {Plane} {Partitions}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {12},
year = {2024},
doi = {10.1017/fms.2023.131},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.131/}
}
TY - JOUR AU - Daoji Huang AU - Jessica Striker TI - A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions JO - Forum of Mathematics, Sigma PY - 2024 VL - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.131/ DO - 10.1017/fms.2023.131 LA - en ID - 10_1017_fms_2023_131 ER -
%0 Journal Article %A Daoji Huang %A Jessica Striker %T A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions %J Forum of Mathematics, Sigma %D 2024 %V 12 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.131/ %R 10.1017/fms.2023.131 %G en %F 10_1017_fms_2023_131
Daoji Huang; Jessica Striker. A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2023.131
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