Fedor B. Lyudogovskiy

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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…

math.GM2026

Numerical topology of the clique complex of the partition graph: Euler characteristic, clique counts, and sequence data

Fedor B. Lyudogovskiy

We study the numerical topology of the clique complex $K_{n} = Cl (G_{n})$ , where $G_{n}$ is the partition graph on the set of integer partitions of $n$ . Building on the previously…

math.GM2026

Morphogenesis Across n: Overlays, Emergence Thresholds, and Weak Self-Similarity in the Partition Graph

Fedor B. Lyudogovskiy

We study the partition graphs $G_{n}$ as a growing family of discrete geometric objects and introduce a formal framework for comparing their structures across different levels. The m…

math.GM2026

Directional Geometry and Anisotropy in the Partition Graph

Fedor B. Lyudogovskiy

We develop a directional formalism for the partition graph G_n based on several canonical reference sets: the main chain, the self-conjugate axis, the spine, and the boundary frame…