Julian D. Allagan

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math.CO2026

Iterating the Lehmer code on inversion sequences: Catalan fixed points and finite stabilization

Julian Allagan, Shanzhen Gao, Benjamin Testart

We study an operator $Θ$ on finite integer sequences, where $Θ (σ)_{i}$ counts the entries to the left of $σ_{i}$ that are strictly smaller than $σ_{i}$ . This operator is a variant of the…

math.CO2025

Strong Central 2-Trees with Tail Degrees {2, 3}: Structural Characterization and Uniqueness Criteria

Julian Allagan, Shawn Langley, Weizheng Gao +1

We study strong $r$ -central $2$ -trees whose non-central vertices have degrees in ${2, 3}$ , focusing on the cases $r = 1, 2, 3$ . For each $r$ , we derive exact degree constraints relati…