Some relational structures with polynomial growth and their associated algebras I: Quasi-polynomiality of the profile
| Autor: | Pouzet, Maurice, Thiéry, Nicolas M. |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Electronic Journal of Combinatorics 20(2) 2013 |
| Druh dokumentu: | Working Paper |
| Popis: | The profile of a relational structure $R$ is the function $\varphi_R$ which counts for every integer $n$ the number $\varphi_R(n)$, possibly infinite, of substructures of $R$ induced on the $n$-element subsets, isomorphic substructures being identified. If $\varphi_R$ takes only finite values, this is the Hilbert function of a graded algebra associated with $R$, the age algebra introduced by P. J. Cameron. In this paper we give a closer look at this association, particularly when the relational structure $R$ admits a finite monomorphic decomposition. This setting still encompass well-studied graded commutative algebras like invariant rings of finite permutation groups, or the rings of quasi-symmetric polynomials. We prove that $\varphi_R$ is eventually a quasi-polynomial, this supporting the conjecture that, under mild assumptions on $R$, $\varphi_R$ is eventually a quasi-polynomial when it is bounded by some polynomial. Comment: 31 pages, 1 figure |
| Databáze: | arXiv |
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