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More bijections for Entringer and Arnold families

  • Received: 01 May 2020 Revised: 01 August 2020 Published: 19 October 2020
  • 05A05, 05A15, 05A19

  • The Euler number $ E_n $ (resp. Entringer number $ E_{n,k} $) enumerates the alternating (down-up) permutations of $ \{1,\dots,n\} $ (resp. starting with $ k $). The Springer number $ S_n $ (resp. Arnold number $ S_{n,k} $) enumerates the type $ B $ alternating permutations (resp. starting with $ k $). In this paper, using bijections we first derive the counterparts in André permutations and Simsun permutations for the Entringer numbers $ (E_{n,k}) $, and then the counterparts in signed André permutations and type $ B $ increasing 1-2 trees for the Arnold numbers $ (S_{n,k}) $.

    Citation: Heesung Shin, Jiang Zeng. More bijections for Entringer and Arnold families[J]. Electronic Research Archive, 2021, 29(2): 2167-2185. doi: 10.3934/era.2020111

    Related Papers:

  • The Euler number $ E_n $ (resp. Entringer number $ E_{n,k} $) enumerates the alternating (down-up) permutations of $ \{1,\dots,n\} $ (resp. starting with $ k $). The Springer number $ S_n $ (resp. Arnold number $ S_{n,k} $) enumerates the type $ B $ alternating permutations (resp. starting with $ k $). In this paper, using bijections we first derive the counterparts in André permutations and Simsun permutations for the Entringer numbers $ (E_{n,k}) $, and then the counterparts in signed André permutations and type $ B $ increasing 1-2 trees for the Arnold numbers $ (S_{n,k}) $.



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