Crossings of Set-Partitions and Addition Crossings of Graded-Independent Random Variables
1997 ◽
Vol 08
(05)
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pp. 645-664
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Keyword(s):
We consider a q-deformation, introduced in [7], of the cumulants associated with a linear functional on polynomials; combinatorially, the deformation is defined using crossing numbers of set-partitions. The paper is concerned with the case q = -1. We show that if the linear functional μ : C[X] → C is symmetric (i.e.μ(Xn) = 0 for n odd), then the exponential generating function of the even (-1)-cumulants of μ is equal to [Formula: see text], (as a formal power series in z). We discuss the connection of this fact with the form of independence for (non-commutative) random variables which corresponds to the operation of Z2-graded tensor product.
2003 ◽
Vol 13
(07)
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pp. 1853-1875
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1983 ◽
Vol 94
(3-4)
◽
pp. 251-263
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Keyword(s):
2016 ◽
Vol 19
(02)
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pp. 1650011
Keyword(s):
2014 ◽
Vol 59
(2)
◽
pp. 553-562
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1985 ◽
Vol 29
(4)
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pp. 707-718
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Keyword(s):