Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps
Solving the first nonmonotonic, longer-than-three instance of a classic enumeration problem, we obtain the generating functionH(x) of all 1342-avoiding permutations of lengthnas well as anexactformula for their numberSn(1342). While achieving this, we bijectively prove that the number of indecomposa...
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| Vydané v: | Journal of combinatorial theory. Series A Ročník 80; číslo 2; s. 257 - 272 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Inc
01.11.1997
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| ISSN: | 0097-3165, 1096-0899 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Solving the first nonmonotonic, longer-than-three instance of a classic enumeration problem, we obtain the generating functionH(x) of all 1342-avoiding permutations of lengthnas well as anexactformula for their numberSn(1342). While achieving this, we bijectively prove that the number of indecomposable 1342-avoiding permutations of lengthnequals that of labeled plane trees of a certain type onnvertices 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 (Can. J. Math.33(1963), 249–271). Moreover,H(x) turns out to be algebraic, proving the first nonmonotonic, longer-than-three instance of a conjecture of Noonan and Zeilberger (Adv. Appl. Math.17(1996), 381–407). We also prove thatSn(1342)converges to 8, so in particular, limn→∞(Sn(1342)/Sn(1234))=0. |
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| ISSN: | 0097-3165 1096-0899 |
| DOI: | 10.1006/jcta.1997.2800 |