TY - JOUR
T1 - Sign imbalances of snakes and valley-signed permutations
AU - Chang, Huilan
AU - Eu, Sen Peng
AU - Lo, Yuan Hsun
N1 - Funding Information:
Partially supported by National Science Council of Taiwan under grants NSC 101-2115-M-390-004-MY3 (S.-P. Eu and Y.-H. Lo) and NSC 100-2115-M-390-004-MY2 (H. Chang).
PY - 2014/8
Y1 - 2014/8
N2 - 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, inv o, invs, invB, and invD.
AB - 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, inv o, invs, invB, and invD.
KW - Alternating permutation
KW - Inversions
KW - Sign imbalance
KW - Snake
KW - Valley-signed permutation
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U2 - 10.1016/j.aam.2014.05.004
DO - 10.1016/j.aam.2014.05.004
M3 - Article
AN - SCOPUS:84905592525
SN - 0196-8858
VL - 59
SP - 26
EP - 47
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
ER -