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Algebraic properties and dismantlability of finite posets

✍ Scribed by Benoit Larose; László Zádori

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
554 KB
Volume
163
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

We show that every finite connected poser which admits certain operations such as Gumm or J6nsson operations, or a near unanimity function is dismantlable. This result is used to prove that a finite poset admits Gumm operations if and only if it admits a near unanimity function. Finite connected posets satisfying these equivalent conditions are characterized by the property that their idempotent subalgebras are dismantlable. As a consequence of these results we obtain that the pro01em of determining if a finite poset admits a near unanimity function is decidable.

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## Abstract A hereditary property of combinatorial structures is a collection of structures (e.g., graphs, posets) which is closed under isomorphism, closed under taking induced substructures (e.g., induced subgraphs), and contains arbitrarily large structures. Given a property $\cal {P}$, we write