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Noncommutative inclusion–exclusion, representations of left regular bands and the Tsetlin library
International Journal of Algebra and Computation ( IF 0.5 ) Pub Date : 2020-09-13 , DOI: 10.1142/s021819672150003x
Guy Blachar 1 , Louis H. Rowen 1 , Uzi Vishne 1
Affiliation  

We find a semigroup [Formula: see text], whose category of partial representations contains the representation category [Formula: see text] of the free left regular band [Formula: see text]. We use this to construct a resolution for the absolute kernel of a representation of [Formula: see text], for which the kernel [Formula: see text] of the Markov operation in the Tsetlin library model is a prominent example. We obtain a formula for the dimension of the absolute kernel, generalizing the equality of the dimension of [Formula: see text] to the number of derangements of order [Formula: see text].

中文翻译:

非交换包含-排除,左正则带的表示和 Tsetlin 库

我们找到一个半群 [Formula: see text],其部分表示的范畴包含自由左正则带 [Formula: see text] 的表示范畴 [Formula: see text]。我们使用它来构造[公式:参见文本]表示的绝对内核的解析,其中Tsetlin库模型中马尔可夫运算的内核[公式:参见文本]是一个突出的例子。我们得到了一个绝对核维数的公式,将[公式:见文本]的维数等式推广到有序紊乱的数量[公式:见文本]。
更新日期:2020-09-13
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