Dey, HK and Sivasubramanian, S
(2023)
*On the alternating runs polynomial in type B and type D Coxeter groups.*
In: Journal of the Ramanujan Mathematical Society, 38
(3).
pp. 215-223.

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## Abstract

Let Rn(t) denote the polynomial enumerating alternating runs in the symmetric group Sn. Wilf showed that (1+t)m divides Rn(t) where m = â��(nâ��2)/2â��. BÃ³na recently gave a group-action-based proof of this fact. In this work, we give a group-action-based proof for type B and type D analogues of this result. Interestingly, our proof gives a group action on the positive/negative parts BÂ±n and DÂ±n and so we get refinements of the result to the case when summation is over BÂ±n and DÂ±n . We are unable to get a group-action-based proof of Wilfâ��s result when summation is over the alternating group An and over Snâ��An, but using other ideas, give a different proof. We give similar results to the polynomial which enumerates alternating sequences in An, Snâ��An, BÂ±n and DÂ±n . As a corollary, we get moment type identities for coefficients of such polynomials. Â© 2023 Ramanujan Mathematical Society. All rights reserved.

Item Type: | Journal Article |
---|---|

Publication: | Journal of the Ramanujan Mathematical Society |

Publisher: | Ramanujan Mathematical Society |

Additional Information: | The copyright for this article belongs toRamanujan Mathematical Society. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 29 Feb 2024 11:41 |

Last Modified: | 29 Feb 2024 11:41 |

URI: | https://eprints.iisc.ac.in/id/eprint/83812 |

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