Geodesic
The Gaussian coefficient revisited
Journal of integer sequences, Tome 19 (2016) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We give a new $q-(1+q)$-analogue of the Gaussian coefficient, also known as the $q$-binomial which, like the original $q$-binomial $\genfrac{[}{]}{0pt}{}{n}{k}_q$, is symmetric in $k$ and $n-k$. We show this $q-(1+q)$-binomial is more compact than the one discovered by Fu, Reiner, Stanton, and Thiem. Underlying our $q-(1+q)$-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birkhoff transform of any finite poset. We end with a discussion of higher analogues of the $q$-binomial.
Classification : 06A07, 05A05, 05A10, 05A30
Keywords: q-analogue, Birkhoff transform, distributive lattice, poset decomposition 
@article{JIS_2016__19_7_a6,
     author = {Ehrenborg, Richard and Readdy, Margaret A.},
     title = {The {Gaussian} coefficient revisited},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {19},
     number = {7},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a6/}
}
TY  - JOUR
AU  - Ehrenborg, Richard
AU  - Readdy, Margaret A.
TI  - The Gaussian coefficient revisited
JO  - Journal of integer sequences
PY  - 2016
VL  - 19
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a6/
LA  - en
ID  - JIS_2016__19_7_a6
ER  - 
%0 Journal Article
%A Ehrenborg, Richard
%A Readdy, Margaret A.
%T The Gaussian coefficient revisited
%J Journal of integer sequences
%D 2016
%V 19
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a6/
%G en
%F JIS_2016__19_7_a6
Ehrenborg, Richard; Readdy, Margaret A. The Gaussian coefficient revisited. Journal of integer sequences, Tome 19 (2016) no. 7. http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a6/