ABSTRACT
The cards are placed on a pile as long as the number x
j
of the card drawn
at the j-th drawing is greater than or equal to the number x
j1
of the card
drawn in the previous drawing; a new pile is started whenever the number
x
j
is less than x
j1
, for j = 1; 2; : : : ;m. The enumeration of the number of
dierent arrangements of the cards that lead to a given number of k piles
is of interest. Clearly, this is a problem of counting the permutations of n
kinds of elements, with s
; s
; : : : ; s
n
elements respectively, which include
k non-decreasing sequences of consecutive elements.
