论文标题
Bernoulli方案的组合编码和Young Tableaux的渐近行为
Combinatorial encoding of Bernoulli schemes and the asymptotic behavior of Young tableaux
论文作者
论文摘要
我们考虑了Bernoulli方案完全可解码的组合编码的两个示例：通过Weyl Sublices编码和更复杂的编码通过RSK（Robinson--Schensted-nuth）对应关系。在第一种情况下，解释性是一个非常简单的事实，而在第二种情况下，这是D. romik和P.〜śniady获得的非平凡结果，并基于论文〜\ cite {kv}，\ cite {vk}等。我们从可衡量分区理论的角度评论证明；使用代表理论和广义二元性二元性的另一个证据将在其他地方介绍。我们还研究了$ P $ -TableAux上Bernoulli变量的新动态，并找到这些tableaux的限制3D形。
We consider two examples of a fully decodable combinatorial encoding of Bernoulli schemes: the encoding via Weyl simplices and the much more complicated encoding via the RSK (Robinson--Schensted--Knuth) correspondence. In the first case, the decodability is a quite simple fact, while in the second case, this is a nontrivial result obtained by D.~Romik and P.~Śniady and based on the papers~ \cite{KV}, \cite{VK}, and others. We comment on the proofs from the viewpoint of the theory of measurable partitions; another proof, using representation theory and generalized Schur--Weyl duality, will be presented elsewhere. We also study a new dynamics of Bernoulli variables on $P$-tableaux and find the limit 3D-shape of these tableaux.
