Abstract
Purchase PDF (1308 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (4)
Purchase PDF (3548 K)
doi:10.1016/S0012-365X(97)00275-6 
Copyright © 1998 Published by Elsevier Science B.V.
Contributions
Steep polyominoes, q-Motzkin numbers and q-Bessel functions*1
Received 22 February 1996;
References and further reading may be available for this article. To view references and further reading you must purchase this article.
Abstract
We introduce three definitions of q-analogs of Motzkin numbers and illustrate some combinatorial interpretations of these q-numbers. We relate the first class of q-numbers to the generating function for steep parallelogram polyominoes according to their width, perimeter and area. We show that this generating function is the quotient of two q-Bessel functions. The second class of q-Motzkin numbers counts the steep staircase polyominoes according to their area, while the third one enumerates the inversions of steep Dyck words. These enumerations allow us to illustrate various techniques of counting and q-counting.
Author Keywords: q-analogs; Motzkin numbers; Polyominoes; Words and q-Bessel functions
