The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
Analogous to MacMahon’s definition of compositions, the second author, 2000, defined n -color compositions as n -color ordered partitions. Several combinatorial properties of n -color compositions were subsequently found by him, 2003, G. Narang and A.K. Agarwal, 2006, 2008, and C. Shapcott, 2012. Recently, Y. Guo 2012, 2013, studied three restricted n -color composition functions and found generating...
In this paper, we consider combinatorial numbers ( C m , k ) m ≥ 1 , k ≥ 0 , mentioned as Catalan triangle numbers where C m , k ≔ m − 1 k − m − 1 k − 1 . These numbers unify the entries of the Catalan triangles B n , k and A n , k for appropriate values of parameters m and k , i.e., B n , k = C 2 n , n − k and A n ,...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.