Geodesic
Generalized Narayana polynomials and their $q$-analogues
Prikladnaya Diskretnaya Matematika. Supplement, no. 9 (2016), pp. 6-8

Voir la notice de l'article provenant de la source Math-Net.Ru

Generating polynomials of the statistics $\mathrm{rise}$, $\mathrm{des}$ and $\mathrm{inv}$ are considered on the entered $312$-avoiding GS-permutations of an order $r\geq1$. It is shown that the polynomials of the statistics $\mathrm{rise}$ and $\mathrm{des}$ are some generalizations of the known Narayana polynomials. For the generalized Narayana polynomials, the inverse generating function, an algebraic equation for the generating function and a recursion relation with multiple convolutions are obtained. For the generating polynomials of pair $\mathrm{(des,inv)}$, an analogue of the obtained recursion relation and an equation for the generating function of these polynomials are found. Their particular case leads to the corresponding $q$-analogues of generalized Narayana polynomials.
Keywords: $312$-avoiding GS-permutations, generalized Narayana polynomials, generating function, inverse function
Mots-clés : convolution, $q$-analogues. 
@article{PDMA_2016_9_a0,
     author = {L. N. Bondarenko and M. L. Sharapova},
     title = {Generalized {Narayana} polynomials and their $q$-analogues},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {6--8},
     publisher = {mathdoc},
     number = {9},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2016_9_a0/}
}
TY  - JOUR
AU  - L. N. Bondarenko
AU  - M. L. Sharapova
TI  - Generalized Narayana polynomials and their $q$-analogues
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2016
SP  - 6
EP  - 8
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2016_9_a0/
LA  - ru
ID  - PDMA_2016_9_a0
ER  - 
%0 Journal Article
%A L. N. Bondarenko
%A M. L. Sharapova
%T Generalized Narayana polynomials and their $q$-analogues
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2016
%P 6-8
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2016_9_a0/
%G ru
%F PDMA_2016_9_a0
L. N. Bondarenko; M. L. Sharapova. Generalized Narayana polynomials and their $q$-analogues. Prikladnaya Diskretnaya Matematika. Supplement, no. 9 (2016), pp. 6-8. http://geodesic.mathdoc.fr/item/PDMA_2016_9_a0/