We extend the classical coupon collectorâ€™s problem to one in which two collectors are simultaneously and independently seeking collections of d coupons. We find, in finite terms, the probability thatâ€¦ (More)

In how many permutations does the pattern Ï„ occur exactly m times? In most cases, the answer is unknown. When we search for rigid patterns, on the other hand, we obtain exact formulas for theâ€¦ (More)

In an influential 1981 paper, Guibas and Odlyzko constructed a generating function for the number of length n strings over a finite alphabet that avoid all members of a given set of forbiddenâ€¦ (More)

A permutation Ïƒ = Ïƒ1Ïƒ2 . . . Ïƒn of n letters contains the pattern Ï„ = Ï„1Ï„2 . . . Ï„k of k letters if for some i1 < i2 < Â· Â· Â· < ik we have Ïƒis < Ïƒit whenever Ï„s < Ï„t. A permutation is said to avoidâ€¦ (More)