Bibliographic Details
| Title: |
The MacMahon q-Catalan is Convex. |
| Authors: |
Amdeberhan, Tewodros1 (AUTHOR) tamdeber@tulane.edu, Wagner, Stephan2 (AUTHOR) |
| Source: |
Annals of Combinatorics. Sep2024, Vol. 28 Issue 3, p1003-1019. 17p. |
| Subject Terms: |
*PARTITION functions, *GENERATING functions, *POLYNOMIALS, *INTEGERS |
| Abstract: |
Let n ≥ 2 be an integer. We prove the convexity of the so-called MacMahon q-Catalan polynomials C n (q) = 1 [ n + 1 ] q 2 n n q viewed as functions of q over the entire set of reals. Along the way, several auxiliary properties of the q-Catalan polynomials and intermediate results in the form of inequalities are presented, with the aim to make the paper self-contained. We also include a commentary on the convexity of the generating function for the integer partitions. [ABSTRACT FROM AUTHOR] |
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