论文标题
加权交换距离的基础对
Weighted exchange distance of basis pairs
论文作者
论文摘要
两对不相交的基础$ \ MATHBF {P} _1 =（R_1，B_1）$和$ \ MathBf {p} _2 =（R_2，B_2，B_2，B_2）$，如果$ \ Mathbf {p} _1 $可以通过$ \ math的$ \ mater} {交流。 1980年，怀特（White）猜想，只要$ r_1 \ cup b_1 = r_2 \ cup b_2 $，始终存在这样的序列。 Hamidoune提出了对猜想的加强，指出交换的最小长度最多是Matroid的等级。 我们提出了Hamidoune猜想的加权变体，其中交换的重量取决于交换元素的权重。我们证明了几个矩形类别的猜想：强烈的基础有序矩形，分裂的矩形，车轮的图形矩形和尖峰。
Two pairs of disjoint bases $\mathbf{P}_1=(R_1,B_1)$ and $\mathbf{P}_2=(R_2,B_2)$ of a matroid $M$ are called equivalent if $\mathbf{P}_1$ can be transformed into $\mathbf{P}_2$ by a series of symmetric exchanges. In 1980, White conjectured that such a sequence always exists whenever $R_1\cup B_1=R_2\cup B_2$. A strengthening of the conjecture was proposed by Hamidoune, stating that minimum length of an exchange is at most the rank of the matroid. We propose a weighted variant of Hamidoune's conjecture, where the weight of an exchange depends on the weights of the exchanged elements. We prove the conjecture for several matroid classes: strongly base orderable matroids, split matroids, graphic matroids of wheels, and spikes.
