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Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face $F \\subsetneq P$ intersects at least $\\dim(F) + 1$ of the polytopes $D_i$. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.\n  Motivated by relaxing the bound $\\dim(F) + 1$ to $\\dim(F)$, we prove a combinatorial formula for the ","authors_text":"Fedor Selyanin","cross_cats":["math.AG"],"headline":"A combinatorial formula is proven for the mixed volume of semi-interlaced polytopes, including those arising in algebraic degree computations via Kouchnirenko-Bernshtein theory.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T12:05:38Z","title":"Semi-interlaced polytopes"},"references":{"count":47,"internal_anchors":9,"resolved_work":47,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"B. Beler, A. Enge, K. Fukuda, Exact Volume Computation for Polytopes: A Practical Study. In: G. Kalai, G.M. Ziegler (eds.) 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