Fedor B. Lyudogovskiy

collaborators

16 papers

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.GM2026

Simplex Layers and Phase Boundaries in the Partition Graph

Fedor B. Lyudogovskiy

For the partition graph $G_{n}$ on the set of partitions of $n$ , we study the stratification induced by the local simplex dimension $dim_{loc} (I^»)$ , defined as the maximal…

math.GM2026

Simplicial shells and thickness in 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 given by elementary transfers of one unit between parts, followed by reor…

math.GM2026

Degree theory of the partition graph: exact maxima, profiles, and fibres

Fedor B. Lyudogovskiy

For the partition graph $G_{n}$ , whose vertices are the partitions of $n$ and whose edges correspond to elementary unit transfers between parts, we develop a degree theory with three…