Catalan numbers are defined by The formula $C_{n}=\frac{1}{n+1}\binom{2n}{n}$. In this paper after some explanations about these numbers and The $q$-analogue, We show that $C_{n}$ is equal to the degree of an irreduable character of the symmetric group and its $q$-analogue involved in the degree of an irreduable character of the general liner group.
Darafsheh, M. (2026). q-Analogue and the Catalan numbers. Journal of Advanced Mathematical Modeling, 16(3), 23–31. https://doi.org/10.22055/jamm.2026.52408.2508
MLA
Darafsheh, M. "q-Analogue and the Catalan numbers", Journal of Advanced Mathematical Modeling, 16, 3, 2026, 23–31. doi: 10.22055/jamm.2026.52408.2508
HARVARD
Darafsheh, M. (2026). 'q-Analogue and the Catalan numbers', Journal of Advanced Mathematical Modeling, 16(3), pp. 23–31. doi: 10.22055/jamm.2026.52408.2508
CHICAGO
Darafsheh, M., "q-Analogue and the Catalan numbers." Journal of Advanced Mathematical Modeling, 16 3 (2026): 23–31, doi: 10.22055/jamm.2026.52408.2508
VANCOUVER
Darafsheh M. q-Analogue and the Catalan numbers. JAMM. 2026;16(3):23–31 (In Persian). doi: 10.22055/jamm.2026.52408.2508
