Self-Dual Symmetric Polynomials and Conformal Partitions
| dc.creator | Fel, Leonid G. | |
| dc.date | 2001-11-13 | |
| dc.date | 2002-01-17 | |
| dc.date.accessioned | 2026-07-07T04:44:34Z | |
| dc.date.available | 2026-07-07T04:44:34Z | |
| dc.description | A conformal partition function ${\cal P}_n^m(s)$, which arose in the theory of Diophantine equations supplemented with additional restrictions, is concerned with {\it self-dual symmetric polynomials} -- reciprocal ${\sf R}^{\{m\}}_ {S_n}$ and skew-reciprocal ${\sf S}^{\{m\}}_{S_n}$ algebraic polynomials based on the polynomial invariants of the symmetric group $S_n$. These polynomials form an infinite commutative semigroup. Real solutions $λ_n(x_i)$ of corresponding algebraic Eqns have many important properties: homogeneity of 1-st order, duality upon the action of the conformal group ${\sf W}$, inverting both function $λ_n$ and the variables $x_i$, compatibility with trivial solution, {\it etc}. Making use of the relationship between Gaussian generating function for conformal partitions and Molien generating function for usual restricted partitions we derived the analytic expressions for ${\cal P}_n^m(s)$. The unimodality indices for the reciprocal and skew-reciprocal equations were found. The existence of algebraic functions $λ_n(x_i)$ invariant upon the action of both the finite group $G\subset S_n$ and conformal group ${\sf W}$ is discussed. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0111155 | |
| dc.identifier | http://arxiv.org/abs/math/0111155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62641 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | primary - 11P81; Secondary - 11N56;20F55 | |
| dc.title | Self-Dual Symmetric Polynomials and Conformal Partitions | |
| dc.type | text |