Monteith Building

Differential posets, introduced in 1988 by Stanley, have a number of remarkable properties. For example, the number of walks that start at the minimal element, go directly to an arbitrary element, and then go directly back to the minimal element, is \(n!\), where \(n\) is the rank of the arbitrary element. Due to this, the two known differential posets – the Young's lattice and the Young-Fibonacci lattice – are the Bratelli diagrams of algebras whose bases are indexed by permutations. The algebra associated to the Young-Fibonacci lattice was introduced by Okada in 1994. In 2024 Florent and Hivert realized a diagram model of the Okada algebra. In this talk we discuss some of the combinatorics associated with these algebras.

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