q-cube enumerator polynomial of Fibonacci cubes

Saygı E., Eğecioğlu O.

DISCRETE APPLIED MATHEMATICS, vol.226, pp.127-137, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 226
  • Publication Date: 2017
  • Doi Number: 10.1016/j.dam.2017.04.026
  • Journal Name: DISCRETE APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.127-137
  • Keywords: Hypercube, Fibonacci number, Fibonacci cube, Cube enumerator polynomial, q-analogue, LUCAS CUBES, DISJOINT HYPERCUBES, JACOBSTHAL
  • Hacettepe University Affiliated: Yes

Abstract

We consider a q-analogue of the cube polynomial of Fibonacci cubes. These bivariate polynomials satisfy a recurrence relation similar to the standard one. They refine the count of the number of hypercubes of a given dimension in Fibonacci cubes by keeping track of the distances of the hypercubes to the all 0 vertex. For q = 1, they specialize to the standard cube polynomials.