On the combinatorics of polynomial generalizations of Rogers-Ramanujan-type identities
type: Item
instance of: scholarly article
title: On the combinatorics of polynomial generalizations of Rogers-Ramanujan-type identities
zbMATH Open document ID: 1006.11058
DOI: 10.1016/S0012-365X(01)00378-8
published in: Discrete Mathematics
publication date: 2002-08-29T00:00:00Z
review text: The author considers the polynomial sequence \(\{P_n(q)\}\), defined inductively by \(P_0(q)=1\), \(P_1(q)= 1+q\), \(P_n(q)= (1-q^2+q^{2n-1}) P_{n-1}(q)+ q^2P_{n-2}(q)\) for \(n\geq 2\). (Setting \(q=1\) yields the Fibonacci sequence.) In addition, the author defines ``Frobenius even alternating'' partitions, and shows that the number of such partitions that are self-conjugate and have largest part at most \(n\) is \(F_n\) (the \(n\)th Fibonacci number).
reviewed by: Neville Robbins
Mathematics Subject Classification ID: 11P84
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 33D15
zbMATH DE Number: 1792477
zbMATH Keywords: Frobenius even alternating partitions
zbMATH Keywords: polynomial generalizations of Rogers-Ramanujan-type identities
zbMATH Keywords: generalized Fibonacci sequence
zbMATH Keywords: q-series
author: Jose Plínio O. Santos
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00378-8
OpenAlex ID: W2039025298
description: scientific article; zbMATH DE number 1792477