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 $dim_{loc} (λ)$ , defined as the maximal d…

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…

math.GM2026

Boundary Framework, Rear Morphology, and Rectangular Ears in the Partition Graph

Fedor B. Lyudogovskiy

We study the outer geometry of the partition graph $G_{n}$ , focusing on its canonical front-and-side framework, the family of nontrivial rectangular partitions, and the rear structur…

math.GM2026

The Degree Landscape of the Partition Graph: Maximal Degree, Extremal Vertices, and Spectra

Fedor B. Lyudogovskiy

We study the degree landscape of the partition graph $G_{n}$ , whose vertices are the integer partitions of $n$ and whose edges correspond to elementary transfers of one unit between…

math.GM2026

Simplex Stratification and Phase Boundaries in the Partition Graph

Fedor B. Lyudogovskiy

We study the partition graph $G_{n}$ , whose vertices are the integer partitions of $n$ and whose edges correspond to elementary transfers of one unit between parts. We introduce the…

math.GM2026

Axial Morphology of the Partition Graph: Self-Conjugate Axis, Spine, and Concentration

Fedor B. Lyudogovskiy

We study the partition graph $G_{n}$ , whose vertices are the partitions of $n$ and whose edges correspond to elementary unit transfers between parts. We define the self-conjugate axi…

math.GM2026

The Partition Graph as a Growing Discrete Geometric Object

Fedor B. Lyudogovskiy

For each positive integer $n$ , let $G_{n}$ be the graph of integer partitions of $n$ , where two partitions are adjacent if one is obtained from the other by an elementary transfer of…

math.GM2026

Local Morphology of the Partition Graph

Fedor B. Lyudogovskiy

For a fixed integer $n$ , let $G_{n}$ be the graph whose vertices are the partitions of $n$ , with adjacency defined by a single elementary transfer of a cell in the Ferrers diagram. I…