A Generalization of Polya's Enumeration Theorem or the Secret Life of Certain Index Sets
| dc.creator | Iliev, Valentin Vankov | |
| dc.date | 1999-02-12 | |
| dc.date.accessioned | 2026-07-07T05:27:53Z | |
| dc.date.available | 2026-07-07T05:27:53Z | |
| dc.description | Polya's fundamental enumeration theorem is generalized in terms of Schur-Macdonald's theory (S-MT) of invariant matrices. Given a permutation group $W\leq S_d$ and a one-dimensional character $χ$ of $W$, the polynomial functor $F_χ$ corresponding via S-MT to the induced monomial representation $U_χ= ind_W^{S_d}(χ)$ of $S_d$, is studied. It turns out that the characteristic $ch(F_χ)$ is the weighted inventory of some set $J(χ)$ of $W$-orbits in the integer-valued hypercube $[0,\infty)^d$. The elements of $J(χ) can be distinguished among all $W$-orbits by a maximum property. The identity $ch(F_χ) = ch(U_χ)$ of both characteristics is a consequence of S-MT. Polya's theorem can be obtained from the above identity by specialization $χ=1_W$, where $1_W$ is the unit character of $W$. | |
| dc.description | 10 pages, uses vanilla.sty | |
| dc.identifier | https://arxiv.org/abs/math/9902075 | |
| dc.identifier | http://arxiv.org/abs/math/9902075 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78093 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 20C30 | |
| dc.title | A Generalization of Polya's Enumeration Theorem or the Secret Life of Certain Index Sets | |
| dc.type | text |