Quasisymmetric expansion of Hall-Littlewood symmetric functions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914996520222720 |
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| author | Grinberg, Darij Vassilieva, Ekaterina A. |
| author_facet | Grinberg, Darij Vassilieva, Ekaterina A. |
| contents | In our previous works we introduced a $q$-deformation of the generating functions for enriched $P$-partitions. We call the evaluation of this generating functions on labelled chains, the $q$-fundamental quasisymmetric functions. These functions interpolate between Gessel's fundamental ($q=0$) and Stembridge's peak ($q=1$) functions, the natural quasisymmetric expansions of Schur and Schur's $Q$-symmetric functions. In this paper, we show that our $q$-fundamental functions provide a quasisymmetric expansion of Hall-Littlewood $S$-symmetric functions with parameter $t=-q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasisymmetric expansion of Hall-Littlewood symmetric functions Grinberg, Darij Vassilieva, Ekaterina A. Combinatorics 05E05, 06A11 In our previous works we introduced a $q$-deformation of the generating functions for enriched $P$-partitions. We call the evaluation of this generating functions on labelled chains, the $q$-fundamental quasisymmetric functions. These functions interpolate between Gessel's fundamental ($q=0$) and Stembridge's peak ($q=1$) functions, the natural quasisymmetric expansions of Schur and Schur's $Q$-symmetric functions. In this paper, we show that our $q$-fundamental functions provide a quasisymmetric expansion of Hall-Littlewood $S$-symmetric functions with parameter $t=-q$. |
| title | Quasisymmetric expansion of Hall-Littlewood symmetric functions |
| topic | Combinatorics 05E05, 06A11 |
| url | https://arxiv.org/abs/2406.01166 |