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Parcial de Combinatoria Algebraica Marzo 4, 2003
 

Summary: Parcial de Combinatoria Algebraica
Marzo 4, 2003
Problemas
1. Decimos que una permutaci’on a 1 . . . a n es alternante si a 1 < a 2 > a 3 < a 4 > · · ·. Sea E n
el n’umero de permutaciones alternantes de [n].
(a) Demuestre que
2E n+1 =
n
#
k=0
# n
k
# E k E n-k .
(b) Concluya que
#
n#0
E n
x n
n!
= tan x + sec x.

  

Source: Ardila, Federico - Department of Mathematics, San Francisco State University

 

Collections: Mathematics