Discrete Mathematics - Special volume: algebraic combinatorics
The Homology of Partitions with an Even Number of Blocks
Journal of Algebraic Combinatorics: An International Journal
A sequence of series for the Lambert W function
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Polynomials with real zeros and Pólya frequency sequences
Journal of Combinatorial Theory Series A
Refined sign-balance on 321-avoiding permutations
European Journal of Combinatorics - Special issue on combinatorics and representation theory
On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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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 Polya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.