Some graph theoretical aspects of generalized truncations

On the chromatic index of generalized truncations

We examine the chromatic index of generalized truncations of graphs and multigraphs.

广义图截断的对称性

Symmetry properties of generalized graph truncations

该研究探讨广义图截断构造中，替换k正则图Γ顶点的k阶图Υ副本所生成图的对称性，及其与Γ和Υ对称性的关联，并通过分类特定围长的三次顶点传递图验证了结果的实用性。

Syntactic aspects of hypergraph polytopes

This paper introduces an inductively defined tree notation for all the faces of polytopes arising from a simplex by truncations. This notation allows us to view inclusion of faces as the process of contracting tree edges. Our notation instantiates to the well-known notations for the faces of associahedra and permutohedra. Various authors have independently introduced combinatorial tools for describing such polytopes. We build on the particular approach developed by Dosen and Petric, who used the formalism of hypergraphs to describe the interval of polytopes from the simplex to the permutohedro…

广义中心三项式系数的解析性质

Analytic aspects of generalized central trinomial coefficients

本文研究广义中心三项式系数的解析性质，证明普通中心三项式多项式只有实根且根交错，并给出广义系数构成对数凸或Stieltjes矩序列的充要条件。

Classical aspects of quantum cohomology of generalized flag varieties

We show that various genus zero Gromov-Witten invariants for flag varieties representing different homology classes are indeed the same. In particular, many of them are classical intersection numbers of Schubert cycles.

On some enumerative aspects of generalized associahedra

We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky to a finite root system and (b) the lattice of noncrossing partitions associated to the corresponding finite real reflection group.