| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Combinatorics
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| Title: |
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Bijections between different models for Entringer numbers |
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| Author(s): |
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Yoann Gelineau ( ) 1, Heesung Shin () 1, Jiang Zeng () 1 |
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| Laboratory: |
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| 1: |
Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX |
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France |
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| Abstract: |
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The Seidel-Entringer triangle is a double indexed sequence $(E_{n,k})$ refining the Euler numbers, whose combinatorial interpretation in alternating permutations was first given by Andr\'{e}. A refinement of Andr\'{e}'s interpretation for $E_{n,k}$ was given by Entringer, who proved that these numbers count alternating permutations according to the first element. In a series of papers, Poupard provided more combinatorial interpretations for $E_{n,k}$ by analytic methods or induction. The aim of this paper is to provide bijections between the different models for $E_{n,k}$. In particular, we establish the first one-to-one correspondence between Entringer's alternating permutations model and Poupard's 0-1-2 increasing trees model. |
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| Fulltext language: |
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English |
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| Production date: |
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2010-04-09 |
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| Keyword(s): |
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Entringer numbers – Euler numbers – alternating permutations – 0-1-2 increasing words – direct alternating permutations – G-words – R-words – U-words |
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| Classification: |
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05A05, 05A19, 05C05 |
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| Comment: |
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19 pages |
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