## Mahler's expansion and Boolean functions

### Summary

Summary: The substitution of $X$ by $X^{2}$ in binomial polynomials generates sequences of integers by Mahler's expansion. We give some properties of these integers and a combinatorial interpretation with covers by projection. We also give applications to the classification of boolean functions. This sequence arose from our previous research on classification and complexity of Binary Decision Diagrams (BDD) associated with boolean functions.

05A10, 94C10

### Keywords/Phrases

mahler's expansion, binomial polynomials, Boolean functions, BDD, enumeration, complexity