TL;DR
This paper investigates the properties of chain posets derived from Boolean algebra and isotropic flags, demonstrating they satisfy the strong Sperner property and are rank-log concave, contributing to combinatorial poset theory.
Contribution
It establishes that chain posets from these specific structures possess the strong Sperner property and are rank-log concave, revealing new combinatorial properties.
Findings
Chain posets from Boolean algebra satisfy the strong Sperner property.
Chain posets from isotropic flags satisfy the strong Sperner property.
Both types of chain posets are rank-log concave.
Abstract
A chain poset, by definition, consists of chains of ordered elements in a poset. We study the chain posets associated to two posets: the Boolean algebra and the poset of isotropic flags. We prove that, in both cases, the chain posets satisfy the strong Sperner property and are rank-log concave.
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Taxonomy
TopicsMathematics and Applications