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Semi-Interlaced Polytopes
Moscow Mathematical Journal. 2026. Vol. 26. No. 2. P. 167–187.
Fedor Selyanin
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we prove a combinatorial formula for the mixed volume of a broad class of semi-interlaced polytopes. This class includes, in particular, the off-coordinate polytopes used in computing algebraic degrees—such as Maximum Likelihood, Euclidean Distance, and Polar degrees—via the Kouchnirenko–Bernshtein theory. We also present applications of our results to the Arnold monotonicity problem (Problem 1982-16), which concerns the dependence of Milnor numbers on the Newton polyhedra
Publication based on the results of:
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We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh–Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial ...
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The group reduction procedure is applied to vector generalizations of the NLS, mKdV,
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We consider Novikov equations for commutative ring generated by differential operators of
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We continue the study of non-Abelian vortex string in 4D N ¼ 2 supersymmetric QCD (SQCD) as critical superstring, and extend this analysis to UðNÞ gauge theory with arbitrary even N and Nf ¼ 2N number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by ...
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Bitter I., Konakov V., Mathematical notes 2026 Vol. 120 No. 4 P. 599–615
The paper provides a generalization of the local limit theorem on the convergence
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Singapore: Springer, 2025.
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., / Series arXiv "math". 2025. No. 2511.20141.
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Esterov A. I., Lang L., Selecta Mathematica, New Series 2022 Vol. 28 No. 2 Article 22
We introduce a new technique to prove connectivity of subsets of covering spaces (so called inductive connectivity), and apply it to Galois theory of problems of enumerative geometry.
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We construct a certain $F_2$-valued analogue of the mixed volume of lattice polytopes. This 2-mixed volume cannot be defined as a polarization of any kind of an additive measure, or characterized by any kind of its monotonicity properties, because neither of the two makes sense over $F_2$. In this sense, the convex-geometric nature of the ...
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If the complement of a closed convex set in a closed convex cone is bounded, then this complement minus the apex of the cone is called a coconvex set. Coconvex sets appear in singularity theory (they are closely related to Newton diagrams) and in commutative algebra. Such invariants of coconvex sets as volumes, mixed volumes, ...
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