Some combinatorial results involving Young diagrams
Some combinatorial results involving Young diagrams
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一些涉及杨氏图的组合结果
DOI：
10.1017/s0305004100054220
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发表时间：
1978
影响因子：
0.8
通讯作者：
Gordon James
中科院分区：
文献类型：
--
作者：
Gordon James
本文的前半部分介绍了一种新的检验Young图的q-钩结构的方法，并用它证明了关于q-核和q-子的大多数标准结果。特别地，我们给出了Chung猜想（2）的一个快速的新证明，该猜想确定了具有给定q-权的图的数量，并说明其中有多少是q-正则的。在q是素数的情况下，这告诉我们在给定的q-块中有多少个对称群的普通和q-模不可约表示。第2节的结果都不是原创的。在下一节中，我们给出了一个新的定义，p-幂图，它与p-商密切相关。这个概念是有趣的，因为当p是素数的条件涉及的p-权力图似乎是一个必要和充分的标准图是p-经常和相应的普通不可约表示保持不可约模p.在本文中，我们得出组合的结果涉及的p-权力图，并在稍后的文章中，我们调查相关的表示理论。
In the first half of this paper we introduce a new method of examining the q-hook structure of a Young diagram, and use it to prove most of the standard results about q-cores and q-quotients. In particular, we give a quick new proof of Chung's Conjecture (2), which determines the number of diagrams with a given q-weight and says how many of them are q-regular. In the case where q is prime, this tells us how many ordinary and q-modular irreducible representations of the symmetric group there are in a given q-block. None of the results of section 2 is original. In the next section we give a new definition, the p-power diagram, which is closely connected with the p-quotient. This concept is interesting because when p is prime a condition involving the p-power diagram appears to be a necessary and sufficient criterion for the diagram to be p-regular and the corresponding ordinary irreducible representation of to remain irreducible modulo p. In this paper we derive combinatorial results involving the p-power diagram, and in a later article we investigate the relevant representation theory.