Some relational structures with polynomial growth and their associated algebras
| dc.creator | Pouzet, Maurice | |
| dc.creator | Thiéry, Nicolas M. | |
| dc.date | 2006-01-11 | |
| dc.date.accessioned | 2026-07-07T06:58:48Z | |
| dc.date.available | 2026-07-07T06:58:48Z | |
| dc.description | The profile of a relational structure R is the function phi_R which counts for every integer n the number, possibly infinite, phi_R(n) of substructures of R induced on the n-element subsets, isomorphic substructures being identified. Several graded algebras can be associated with R in such a way that the profile of R is simply the Hilbert function. An example of such graded algebra is 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 decomposes into finitely many monomorphic components. In this case, several well-studied graded commutative algebras (e.g. the invariant ring of a finite permutation group, the ring of quasi-symmetric polynomials) are isomorphic to some age algebras. Also, phi_R is a quasi-polynomial, this supporting the conjecture that, with mild assumptions on R, phi_R is a quasi-polynomial when it is bounded by some polynomial. | |
| dc.description | 20 pages. Presented at FPSAC'05 Taormina, June 2005 | |
| dc.identifier | https://arxiv.org/abs/math/0601256 | |
| dc.identifier | http://arxiv.org/abs/math/0601256 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107502 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.title | Some relational structures with polynomial growth and their associated algebras | |
| dc.type | text |