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Exact Enumeration Of 1342Avoiding Permutations A Close Link With Labeled Trees And Planar Maps
, 1997
"... Solving the first nonmonotonic, longerthanthree instance of a classic enumeration problem, we obtain the generating function H(x) of all 1342avoiding permutations of length n as well as an exact formula for their number Sn (1342). While achieving this, we bijectively prove that the number of inde ..."
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Cited by 84 (7 self)
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Solving the first nonmonotonic, longerthanthree instance of a classic enumeration problem, we obtain the generating function H(x) of all 1342avoiding permutations of length n as well as an exact formula for their number Sn (1342). While achieving this, we bijectively prove that the number of indecomposable 1342avoiding permutations of length n equals that of labeled plane trees of a certain type on n vertices recently enumerated by Cori, Jacquard and Schaeffer, which is in turn known to be equal to the number of rooted bicubic maps enumerated by Tutte in 1963. Moreover, H(x) turns out to be algebraic, proving the first nonmonotonic, longerthanthree instance of a conjecture of Zeilberger and Noonan. We also prove that n p Sn (1342) converges to 8, so in particular, limn!1 (Sn (1342)=Sn (1234)) = 0.
Priority Queues and Multisets
 ELECTRONIC J. COMBINAT
, 1995
"... A priority queue, a container data structure equipped with the operations insert and deleteminimum, can reorder its input in various ways, depending both on the input and on the sequence of operations used. If a given input oe can produce a particular output ø then (oe; ø ) is said to be an allow ..."
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Cited by 3 (1 self)
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A priority queue, a container data structure equipped with the operations insert and deleteminimum, can reorder its input in various ways, depending both on the input and on the sequence of operations used. If a given input oe can produce a particular output ø then (oe; ø ) is said to be an allowable pair. It is shown that allowable pairs on a fixed multiset are in onetoone correspondence with certain kway trees and, consequently, the allowable pairs can be enumerated. Algorithms are presented for determining the number of allowable pairs with a fixed input component, or with a fixed output component. Finally, generating functions are used to study the maximum number of output components with a fixed input component, and a symmetry result is derived.
Generating Permutations With kDifferences
 SIAM Journal on Discrete Mathematics
, 1989
"... Given (n; k) with n k 2 and k 6= 3, we show how to generate all permutations of n objects (each exactly once) so that successive permutations differ in exactly k positions, as do the first and last permutations. This solution generalizes known results for the specific cases where k = 2 and k = ..."
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Cited by 2 (2 self)
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Given (n; k) with n k 2 and k 6= 3, we show how to generate all permutations of n objects (each exactly once) so that successive permutations differ in exactly k positions, as do the first and last permutations. This solution generalizes known results for the specific cases where k = 2 and k = n. When k = 3, we show that it is possible to generate all even (odd) permutations of n objects so that successive permutations differ in exactly 3 positions. Keywords. permutations, Gray codes, combinatorial algorithms, Cayley graphs, Hamilton cycles AMS(MOS) subject classifications. 05A15, 05C45 1 Introduction The problem of generating permutations of n distinct objects is of fundamental importance both in Computer Science and in Combinatorics. Many practical problems require for their solution a sampling of random permutations or, worse, a search through all n! permutations. In order for such a search to be possible, even for moderate size n, permutation generation methods must be e...