Derived Palintiple Families and Their Palinomials

TL;DR

This paper explores families of palintiples and their associated palinomials, revealing relationships between their digits and roots, and discusses implications for Young graph isomorphism classes.

Contribution

It introduces methods for constructing palintiple families from lower-base types and uncovers direct links between palintiple digits and palinomials' roots.

Findings

Established relationships between palintiple digits and palinomials' roots

Developed construction methods for derived palintiple families

Discussed implications for Young graph isomorphism classes

Abstract

We consider several families of palintiples (also known as reverse multiples) whose carries themselves are digits of lower-base palintiples and give some methods for constructing them from fundamental palintiple types. We also continue the study of palinomials introduced in an earlier paper by revealing a more direct relationship between the digits of certain palintiple types and the roots of their palinomials. We explore the consequences of this relationship for palinomials induced by palintiple families derived from lower-base palintiples. Finally, we pose some questions regarding Young graphs of derived palintiple families and consider the implications our general observations might have for relations between Young graph isomorphism classes.