(2,3)-Cordial Oriented Hypercubes

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. IV

We present statistics on the decompositions (with respect to a distinguished symmetric 2t-cycle) of vertices of the hypercube graph, whose negative parts are covered by two subsets of the ground set {1,...,t} of the corresponding oriented matroid.

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. III

We present statistics on the decompositions (with respect to a distinguished symmetric 2t-cycle) of vertices of the hypercube graph, whose negative parts are regarded as disjoint unions of two subsets of the ground set {1,...,t} of the corresponding oriented matroid.

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. II

We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.

Vertex Turán problems for the oriented hypercube

In this short note we consider the oriented vertex Turán problem in the hypercube: for a fixed oriented graph $\overrightarrow{F}$, determine the maximum size $ex_v(\overrightarrow{F}, \overrightarrow{Q_n})$ of a subset $U$ of the vertices of the oriented hypercube $\overrightarrow{Q_n}$ such that the induced subgraph $\overrightarrow{Q_n}[U]$ does not contain any copy of $\overrightarrow{F}$. We obtain the exact value of $ex_v(\overrightarrow{P_k}, \overrightarrow{Q_n})$ for the directed path $\overrightarrow{P_k}$, the exact value of $ex_v(\overrightarrow{V_2}, \overrightarrow{Q_n})$ for the…

定向拟阵上的模式识别：超立方体图中的对称循环。VI

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. VI

本文探讨二元数组精确模型表示的线性代数、组合与应用层面，并以字符串的两幅线性代数画像加以说明。

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs

If V is the vertex sequence of a symmetric 2t-cycle in the hypercube graph with the vertices {1,-1}^t, then for any vertex T of the graph there exists a unique inclusion-minimal subset of V such that T is the sum of its elements. We present a simple combinatorial statistic on decompositions of vertices of the hypercube graphs with respect to symmetric cycles and describe their basic metric properties.