$q$-enumeration of type B and D Eulerian polynomials based on parity of descents

[2211.15277] $q$-enumeration of type B and D Eulerian polynomials based on parity of descents Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2211.15277 (math) [Submitted on 28 Nov 2022 ( v1 ), last revised 13 Feb 2023 (this version, v3)] Title: $q$-enumeration of type B and D Eulerian polynomials based on parity of descents Authors: Hiranya Kishore Dey , Umesh Shankar , Sivaramakrishnan Sivasubramanian View a PDF of the paper titled $q$-enumeration of type B and D Eulerian polynomials based on parity of descents, by Hiranya Kishore Dey and 2 other authors View PDF HTML (experimental) Abstract: Carlitz and Scoville in 1973 considered a four variable polynomial that enumerates permutations in $\mathfrak{S}_n$ with respect to the parity of its descents and ascents. In recent work, Pan and Zeng proved a $q$-analogue of Carlitz-Scoville's generating function by enumerating permutations with the above four statistice along with the inversion number. Further, they also proved a type B analogue by enumerating signed permutations with respect to the parity of descents and ascents. In this work we prove a $q$-analogue of the type B result of Pan and Zeng by enumerating permutations in $\mathfrak{B}_n$ with the above four statistics and the type B inversion number. We also obtain a $q$-analogue of the generating function for the type B bivariate alternating descent polynomials. We consider a similar five-variable polynomial in the type D Coxeter groups as well and give their egf. Alternating descents for the type D groups were previously also defined by Remmel, but our definition is slightly different. As a by-product of our proofs, we get bivariate $q$-analogues of Hyatt's recurrences for the type B and type D Eulerian polynomials. Further corollaries of our results are some symmetry relations for these polynomials and $q$-analogues of generating functions for snakes of types B and D. Comments: 27 pages. Comments are welcome Subjects: Combinatorics (math.CO) MSC classes: 05A05, 05A15, 05E16 Cite as: arXiv:2211.15277 [math.CO] (or arXiv:2211.15277v3 [math.CO] for this version) https://doi.org/10.48550/arXiv.2211.15277 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Enumerative Combinatorics and Applications, Vol 4, Article #S2R3, 2024 Submission history From: Hiranya Kishore Dey [ view email ] [v1] Mon, 28 Nov 2022 13:05:59 UTC (26 KB) [v2] Mon, 26 Dec 2022 16:57:27 UTC (27 KB) [v3] Mon, 13 Feb 2023 17:56:39 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled $q$-enumeration of type B and D Eulerian polynomials based on parity of descents, by Hiranya Kishore Dey and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2022-11 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• A lower bound for the Call-Silverman height in cyclotomic extensions#822176
• Restricted inversion polynomials#997452
• Partial wave analyses of $ψ(3686)\to p\bar{p}π^0$ and $ψ(3686)\to p\bar{p}η$#141679
• A power-sum obstruction to cyclotomicity in a family of symmetric numerical semigroups#1077413
• Strongly regular graph, strongly polynomial sequences, and two-level polynomials#1116033