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All maximal congruences on an inverse semigroup of fence-preserving transformations

We study the inverse semigroup of all partial injections on an \(n\)-element set \(\{1,...,n\}\), which preserve the zig-zag order \(1\prec 2\succ 3\prec 4\succ \cdots n\) and the parity for some positive integer \(n\). We characterize all maximal congruences on this inverse semigroup, which are ent...

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Bibliographic Details
Date:2026
Main Authors: Chaichompoo, Utsithon, Koppitz, Jörg, Mati, Yananan
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2026
Subjects:
partial injection
inverse semigroup
zig-zag order
maximal congruence
20M20
20M05
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2469
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Journal Title:Algebra and Discrete Mathematics
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Algebra and Discrete Mathematics
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Summary:We study the inverse semigroup of all partial injections on an \(n\)-element set \(\{1,...,n\}\), which preserve the zig-zag order \(1\prec 2\succ 3\prec 4\succ \cdots n\) and the parity for some positive integer \(n\). We characterize all maximal congruences on this inverse semigroup, which are entirely congruences of index two.
DOI:10.12958/adm2469

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