Zero-sum multisets mod p with an application to surface automorphisms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866909960568307712 |
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| author | Weaver, Anthony |
| author_facet | Weaver, Anthony |
| contents | We solve a problem in enumerative combinatorics which is equivalent to counting topological types of certain group actions on compact Riemann surfaces. Let $V_2(F_p)$ be the two-dimensional vector space over $F_p$, the field with $p$ elements, $p$ an odd prime. We count orbits of the general linear group $GL_2(F_p)$ on certain multisets consisting of $R \geq 3$ non-zero columns from $V_2(F_p)$. The $R$-multisets are `zero-sum,' that is, the sum (mod $p$) over the columns in the multiset is $[\begin{smallmatrix} 0 \\ 0 \end{smallmatrix}]$. The orbit count yields the number of topological types of fully ramified actions of the elementary abelian $p$-group of rank $2$ on compact Riemann surfaces of genus $1+ Rp(p-1)/2-p^2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_02147 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Zero-sum multisets mod p with an application to surface automorphisms Weaver, Anthony Combinatorics 05A15, 14J50 We solve a problem in enumerative combinatorics which is equivalent to counting topological types of certain group actions on compact Riemann surfaces. Let $V_2(F_p)$ be the two-dimensional vector space over $F_p$, the field with $p$ elements, $p$ an odd prime. We count orbits of the general linear group $GL_2(F_p)$ on certain multisets consisting of $R \geq 3$ non-zero columns from $V_2(F_p)$. The $R$-multisets are `zero-sum,' that is, the sum (mod $p$) over the columns in the multiset is $[\begin{smallmatrix} 0 \\ 0 \end{smallmatrix}]$. The orbit count yields the number of topological types of fully ramified actions of the elementary abelian $p$-group of rank $2$ on compact Riemann surfaces of genus $1+ Rp(p-1)/2-p^2.$ |
| title | Zero-sum multisets mod p with an application to surface automorphisms |
| topic | Combinatorics 05A15, 14J50 |
| url | https://arxiv.org/abs/1703.02147 |