Sign imbalances of snakes and valley-signed permutations

One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type An is the set of the alternating permutations and in type Bn (or Dn) is the set of certain signed permutations. The set of valley-signed permutations, defined by Josuat-Vergès, Novelli and Thibon,...

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Bibliographic Details
Published in:Advances in applied mathematics 2014-08, Vol.59, p.26-47
Main Authors: Chang, Huilan, Eu, Sen-Peng, Lo, Yuan-Hsun
Format: Article
Language:English
Subjects:
Alternating permutation
Combinatorial analysis
Inversions
Mathematical analysis
Permutations
Sign imbalance
Snake
Snakes
Statistics
Valley-signed permutation
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Summary:One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type An is the set of the alternating permutations and in type Bn (or Dn) is the set of certain signed permutations. The set of valley-signed permutations, defined by Josuat-Vergès, Novelli and Thibon, is another structure counted by the Springer numbers of type Bn (or Dn). In this paper we determine the sign imbalances of these sets of snakes and valley-signed permutations under various inversion statistics invw, invo, invs, invB, and invD.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2014.05.004