Stirling numbers in braid matroid Kazhdan–Lusztig polynomials
نویسندگان
چکیده
منابع مشابه
Applications of Chromatic Polynomials Involving Stirling Numbers
The Stirling numbers of the second kind, denoted S(n, k), are the number of ways to partition n distinct objects into k nonempty subsets. We use the notation [n] = {1, 2,. . ., n} and sometimes refer to the subsets as blocks. The initial conditions are defined as: S(0, 0) = 1, S(n, 0) = 0, for n ≥ 1, and S(n, k) = 0 for k > n. We also have S(n, 2) = 2 n−1 − 1 and S(n, n − 1) = n 2. The numbers ...
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and Applied Analysis 3 and continuing like that to S8. For large n this method is not convenient. However, later that year Ligowski 4 suggested a better method, providing a generating function for the numbers Sn: e z ∞ ∑ k 0 e k! ∞ ∑ k 0 ∞ ∑ n 0 k k! z n! ∞ ∑ n 0 Sn z n! . 2.4 Further, an effective iteration formula was found Sn n−1 ∑ j 0 ( n − 1 j ) Sj 2.5 by which every Sn can be evaluated st...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2019
ISSN: 0196-8858
DOI: 10.1016/j.aam.2018.09.003