Cycles in subexpression graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911158781345792 |
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| author | Shchigolev, Vladimir |
| author_facet | Shchigolev, Vladimir |
| contents | Let $\mathfrak{S}(\underline{s},w)$ be the graph whose vertices are all subexpressions with target $w$ of a fixed expression $\underline{s}$ in generators of a Coxeter group and edges are the pairs of subexpressions with Hamming distance 2. We prove that $\mathfrak{S}(\underline{s},w)$ is connected and its cycle space is spanned by cycles of lengths $d+2$, where $d$ ranges over all positive divisors of all finite orders of products of at most two entries of $\underline{s}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11208 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cycles in subexpression graphs Shchigolev, Vladimir Representation Theory Combinatorics Group Theory Geometric Topology 20F55, 51F15, 05C45, 57M15 Let $\mathfrak{S}(\underline{s},w)$ be the graph whose vertices are all subexpressions with target $w$ of a fixed expression $\underline{s}$ in generators of a Coxeter group and edges are the pairs of subexpressions with Hamming distance 2. We prove that $\mathfrak{S}(\underline{s},w)$ is connected and its cycle space is spanned by cycles of lengths $d+2$, where $d$ ranges over all positive divisors of all finite orders of products of at most two entries of $\underline{s}$. |
| title | Cycles in subexpression graphs |
| topic | Representation Theory Combinatorics Group Theory Geometric Topology 20F55, 51F15, 05C45, 57M15 |
| url | https://arxiv.org/abs/2506.11208 |