Geodesic
Macdonald polynomials at $t=q^k$
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

Voir la notice de l'article provenant de la source Episciences

We investigate the homogeneous symmetric Macdonald polynomials $P_{\lambda} (\mathbb{X} ;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$ and $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q,q^k)$. As a consequence, we describe an operator whose eigenvalues characterize the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$. 
@article{DMTCS_2009_special_256_a9,
     author = {Luque, Jean-Gabriel},
     title = {Macdonald polynomials at $t=q^k$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2687},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2687/}
}
TY  - JOUR
AU  - Luque, Jean-Gabriel
TI  - Macdonald polynomials at $t=q^k$
JO  - Discrete mathematics & theoretical computer science
PY  - 2009
VL  - DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2687/
DO  - 10.46298/dmtcs.2687
LA  - en
ID  - DMTCS_2009_special_256_a9
ER  - 
%0 Journal Article
%A Luque, Jean-Gabriel
%T Macdonald polynomials at $t=q^k$
%J Discrete mathematics & theoretical computer science
%D 2009
%V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2687/
%R 10.46298/dmtcs.2687
%G en
%F DMTCS_2009_special_256_a9
Luque, Jean-Gabriel. Macdonald polynomials at $t=q^k$. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2687. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2687/

Cité par Sources :