Abstract

The Motzkin numbers count the number of lattice paths which go from (0,0) to (n,0) using steps (1,1),(1,0) and (1,−1) and never go below the x-axis. Let Mn,k be the number of such paths with exactly k horizontal steps. We investigate the analytic properties of various combinatorial triangles related to the Motzkin triangle [Mn,k]n,k≥0, including their total positivity, the real-rootedness and interlacing property of the generating functions of their rows, and the asymptotic normality (by central and local limit theorems) of these triangles. We also prove several identities related to these triangles.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.