论文标题
极端刚性蜂窝的枚举
The enumeration of extreme rigid honeycombs
论文作者
论文摘要
Knutson，Tao和Woodward引入了刚性的树蜂窝，并且由Dykema，Collins，Timotin和作者展示为极端刚性蜂窝的总和，并具有独特的确定的总结到排列。如果两个极端的刚性蜂窝基本相同，如果它们具有比例的退出多重性，并且为了确定，这种蜂窝的等效类别可以持续很多。我们描述了处理这些等价类别的两种方法。第一种方法通过查看可以从某个二次二磷剂方程获得的锁定模式来产生所有固定重量的固定树蜂窝的（有限）列表。第二种方法构建了两个刚性树蜂窝的刚性覆盖的任意僵硬的树蜂窝，重量严格较小。原则上，这允许从单位重量开始的所有刚性树蜂窝的感应构造。我们还表明，两种刚性树蜂窝的一些刚性叠加层产生了一个无限的刚性树蜂窝状的序列，具有增加的复杂性，但具有固定数量的非零出口多重性。最后的结果涉及一种新的通货膨胀/通货膨胀构建，还产生了其他无限的刚性树蜂窝序列。
Rigid tree honeycombs were introduced by Knutson, Tao, and Woodward and they were shown by Dykema, Collins, Timotin, and the authors to be sums of extreme rigid honeycombs, with uniquely determined summands up to permutations. Two extreme rigid honeycombs are essentially the same if they have proportional exit multiplicities and, up to this identification, there are countably many equivalence classes of such honeycombs. We describe two ways to approach the enumeration of these equivalence classes. The first method produces a (finite) list of all rigid tree honeycombs of fixed weight by looking at the locking patterns that can be obtained from a certain quadratic Diophantine equation. The second method constructs arbitrary rigid tree honeycombs from rigid overlays of two rigid tree honeycombs with strictly smaller weights. This allows, in principle, for an inductive construction of all rigid tree honeycombs starting with those of unit weight. We also show that some rigid overlays of two rigid tree honeycombs give rise to an infinite sequence of rigid tree honeycombs of increasing complexity but with a fixed number of nonzero exit multiplicities. This last result involves a new inflation/deflation construction that also produces other infinite sequences of rigid tree honeycombs.
