Corpus ID: 11611550

Enumeration of snakes and cycle-alternating permutations

@article{JosuatVergs2014EnumerationOS,
  title={Enumeration of snakes and cycle-alternating permutations},
  author={Matthieu Josuat-Verg{\`e}s},
  journal={Australas. J Comb.},
  year={2014},
  volume={60},
  pages={279-305}
}
Springer numbers are an analog of Euler numbers for the group of signed permutations. Arnol'd showed that they count some objects called snakes, that generalize alternating permutations. Hoffman established a link between Springer numbers, snakes, and some polynomials related with the successive derivatives of trigonometric functions. The goal of this article is to give further combinatorial properties of derivative polynomials, in terms of snakes and other objects: cycle-alternating… Expand
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  • 6
  • Highly Influenced
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  • Computer Science, Mathematics
  • SIAM J. Discret. Math.
  • 2018
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  • 1
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References

SHOWING 1-10 OF 52 REFERENCES
Combinatorial aspects of continued fractions
  • P. Flajolet
  • Computer Science, Mathematics
  • Discret. Math.
  • 1980
  • 439
  • PDF
Crossings of signed permutations and $q$-Eulerian numbers of type $B$
  • 11
  • PDF
The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups
  • 70
  • Highly Influential
Derivative polynomials and enumeration of permutations by number of interior and left peaks
  • Shi-Mei Ma
  • Computer Science, Mathematics
  • Discret. Math.
  • 2012
  • 33
  • PDF
Labeled Ballot Paths and the Springer Numbers
  • 10
  • Highly Influential
  • PDF
Combinatorics of the Three-Parameter PASEP Partition Function
  • 17
  • PDF
A Survey of Alternating Permutations
  • 130
  • Highly Influential
  • PDF
...
1
2
3
4
5
...