Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain   with perfect state transfer
  Analogs of Krawtchouk polynomials defined on a bi-lattice are introduced. They are shown to provide a (novel) spin chain with perfect transfer. Their characterization is given as well as their connection to the quadratic Hahn algebra 
Luc Vinet and Alexei Zhedanov
math-ph math.CA math.MP quant-ph