On enumerators of Smirnov words by descents and cyclic descents
نویسندگان
چکیده
منابع مشابه
Decreases and Descents in Words
The generating function for words by a multivariable statistic involving decrease, increase, descent and rise values is explicitly calculated by using the MacMahon Master Theorem and the properties of the first fundamental transformation on words. Applications to statistical study of the symmetric group are also given.
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Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something that can be called a descent algebra. There is also a commutative, semisimple subalgebra of Solomon’s descent algebra generated by sums of permutations with the sam...
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We prove an identity conjectured by Adin and Roichman involving the descent set of λ-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set ...
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We use Janson’s dependency criterion to prove that the distribution of d-descents of permutations of length n converge to a normal distribution as n goes to infinity. We show that this remains true even if d is allowed to grow with n.
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We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can be expressed as the reciprocal of a sum involving Euler numbers: ( 1− E1x + E3 x3 3! − E4 x4 4! + E6 x6 6! − E7 x7 7! + · · · )−1 , (∗) where ∑∞ n=0Enx n/n! ...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2020
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2020.v11.n3.a1