TY - JOUR
T1 - A refined sign-balance of simsun permutations
AU - Eu, Sen Peng
AU - Fu, Tung Shan
AU - Pan, Yeh Jong
N1 - Funding Information:
The authors thank the referees for carefully reading the manuscript and providing helpful suggestions. This research was partially supported by NSC grants 101-2115-M-390-004 (S.-P. Eu), 101-2115-M-251-001 (T.-S. Fu), and 101-2115- M-127-001 (Y.-J. Pan).
PY - 2014/2
Y1 - 2014/2
N2 - We present a refined sign-balance result for simsun permutations. On the basis of our previously established bijection between simsun permutations and increasing 1-2 trees, we deduce the recurrence relation and exponential generating function for the sign-balance of simsun permutations of length n with k descents. For odd lengths, the distribution turns out to be (shifted) second-order Eulerian numbers. For even lengths, the distribution forms a signed triangle whose row sums are all zeros. Meanwhile, we obtain two Pólya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.
AB - We present a refined sign-balance result for simsun permutations. On the basis of our previously established bijection between simsun permutations and increasing 1-2 trees, we deduce the recurrence relation and exponential generating function for the sign-balance of simsun permutations of length n with k descents. For odd lengths, the distribution turns out to be (shifted) second-order Eulerian numbers. For even lengths, the distribution forms a signed triangle whose row sums are all zeros. Meanwhile, we obtain two Pólya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.
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U2 - 10.1016/j.ejc.2013.05.001
DO - 10.1016/j.ejc.2013.05.001
M3 - Article
AN - SCOPUS:84882937091
SN - 0195-6698
VL - 36
SP - 97
EP - 109
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
ER -