The Generating Function for Total Displacement
نویسندگان
چکیده
منابع مشابه
The Generating Function for Total Displacement
In a 1977 paper, Diaconis and Graham studied what Knuth calls the total displacement of a permutation w, which is the sum of the distances |w(i)−i|. In recent work of the first author and Tenner, this statistic appears as twice the type An−1 version of a statistic for Coxeter groups called the depth of w. There are various enumerative results for this statistic in the work of Diaconis and Graha...
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For an integer t ≥ 1 and a partition λ, we let Ht(λ) be the multiset of hook lengths of λ which are divisible by t. Then, define aeven t (n) and aodd t (n) to be the number of partitions of n such that |Ht(λ)| is even or odd, respectively. In a recent paper, Han generalized the Nekrasov-Okounkov formula to obtain a generating function for at(n) = aeven t (n)− aodd t (n). We use this generating ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/4329