Fan Chung ; Anders Claesson ; Mark Dukes ; Ronald Graham - Descent polynomials for permutations with bounded drop size

dmtcs:2856 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2856
Descent polynomials for permutations with bounded drop sizeArticle

Authors: Fan Chung 1; Anders Claesson 2; Mark Dukes ORCID3,4; Ronald Graham 1

Motivated by juggling sequences and bubble sort, we examine permutations on the set${1, 2, \ldots, n}$ with $d$ descents and maximum drop size $k$. We give explicit formulas for enumerating such permutations for given integers $k$ and $d$. We also derive the related generating functions and prove unimodality and symmetry of the coefficients.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Permutations,descent polynomial,drop size,Eulerian distribution.,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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