Derived palintiple families and their palinomials (Q2830373)

A \((k,b)\)-palintiple (or reverse multiple) is a positive integer \(n\) such that the base \(b\) expansion of \(kn\) is the reversal of that of \(n\). For example, \(1089\) is a \((9,10)\)-palintiple. The \((k,b)\)-palintiples can be determined by the Young graph \(Y(k,b)\). The author provides constructions of \((k',b')\)-palintiples from \((k,b)\)-palintiples and considers the question when \(Y(k,b)\) is isomorphic to \(Y(9,10)\).NEWLINENEWLINEA palinomial is a certain polynomial associated with a palintiple. The author studies the roots of palinomials, as well as relations between the palinomial of a palintiple and the palinomial of a derived palintiple. The paper concludes with several open questions on isomorphism classes of Young graphs.