Fedor B. Lyudogovskiy

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math.CO2026

Local Complexity, Overlap Control, and Global Simplicity in Partition Graphs: A Conceptual Synthesis for G_n and K_n = Cl(G_n)

Fedor B. Lyudogovskiy

For each positive integer $n$ , let $G_{n}$ be the partition graph whose vertices are the partitions of $n$ , with adjacency defined by an elementary transfer of one unit between parts…

math.CO2026

Jump and Gradient Invariants in the Partition Graph

Fedor B. Lyudogovskiy

We introduce edgewise jump invariants and gradient-type structures for the partition graph $G_{n}$ , whose vertices are the partitions of $n$ and whose edges correspond to elementary…

math.CO2026

Support and Support Jumps in the Partition Graph

Fedor B. Lyudogovskiy

Let $G_{n}$ be the partition graph whose vertices are the partitions of $n$ , with adjacency given by elementary transfers of one cell between parts, followed by reordering. We study…

math.CO2026

The homotopy type of the clique complex of the partition graph

Fedor B. Lyudogovskiy

For each positive integer $n$ , let $G_{n}$ be the graph whose vertices are the partitions of $n$ , with edges corresponding to elementary transfers of one cell between two parts, foll…