Subword complexes and 2-truncated cubes

Geometric realization of $γ$-vectors of 2-truncated cubes

This paper continues investigation of the class of flag simple polytopes called 2-truncated cubes. It is an extended version of the short note Volodin (2012). A 2-truncated cube is a polytope obtained from a cube by sequence of truncations of codimension 2 faces. Constructed uniquely defined function which maps any 2-truncated cube to a flag simplicial complex with $f$-vector equal to $γ$-vector of the polytope. As a corollary we obtain that $γ$-vectors of 2-truncated cubes satisfy Frankl-Furedi-Kalai inequalities.

Classification of vertex-transitive cubic partial cubes

Partial cubes are graphs isometrically embeddable into hypercubes. In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: $K_2 \, \square \, C_{2n}$, for some $n\geq 2$, the generalized Petersen graph $G(10,3)$, the cubic permutahedron, the truncated cuboctahedron, or the truncated icosidodecahedron. This classification is a generalization of results of Brešar et al.~from 2004 on cubic mirror graphs, it includes all cubic, distance-regular partial cubes (Weichsel, 1992), and presents a contribution to the classification of all …

A supercongruence involving cubes of Catalan numbers

We mainly show a supercongruence for a truncated series with cubes of Catalan numbers which extends a result by Zhi-Wei Sun.

立方截断的Hadamard单纯形的完整性、光滑性与正规性界

Integrality, smoothness and normality bounds for cube-truncated Hadamard simplices

该研究解决了扩张 Hadamard 单纯形与立方体交集的完整性、光滑性与正规性问题，给出了维度十一的非完整示例、光滑性完全刻画及正规性界，并用 Lean 验证了所有编号结果。