4 papers
math.CO2026
Semi-interlaced polytopes
Fedor Selyanin
The Minkowski mixed volume of subpolytopes of a polytope clearly does not exceed the normalized volume . Equality…
math.CO2025
Newton numbers, vanishing polytopes and algebraic degrees
Fedor Selyanin
Consider a polynomial with a convenient Newton polytope and generic complex coefficients. By the global version of the Kouchnirenko formula, the hypersurface $\{f = 0\} \su…
math.CO2025
B-facets in dimension 4
Fedor Selyanin
We complete the classification of B-facets of a 4-dimensional Newton polyhedron, filling a gap in the classification of arXiv:1309.0630, found by the authors of arXiv:2209.03553.
math.AG2024
Arnold's monotonicity problem
Fedor Selyanin
According to the Kouchnirenko formula, the Milnor number of a generic isolated singularity with given Newton polyhedron is equal to the alternating sum of certain volumes associate…