On arithmetic and asymptotic properties of up–down numbers
نویسندگان
چکیده
منابع مشابه
On arithmetic and asymptotic properties of up-down numbers
Let = ( 1, . . . , N), where i = ±1, and let C( ) denote the number of permutations of 1, 2, . . . , N + 1, whose up–down signature sign( (i + 1)− (i))= i , for i = 1, . . . , N . We prove that the set of all up–down numbers C( ) can be expressed by a single universal polynomial , whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.09.020