# What is the name for a polynomial with all coefficients equal to 1?

I am looking for a good google search word for polynomials that have all coefficients equal to 1.

An example of a such polynomial is:

$$1+x^{23}+x^{57}+x^{101}$$

One such polynomial could also be the special case which is the truncated geometric series:

$$\sum\limits_{n=0}^{n=k} x^n$$

but I am more interested in the irregular form as in the example.

What is the name for a polynomial with all coefficients equal to 1?

• May be, one of these days, they will be called Granvik polynomials. Why not ? I am not kidding you, be sure. Cheers :-) – Claude Leibovici Nov 22 '14 at 15:49
• Maybe you mean all nonzero coefficients equal to one. A polynomial can have only finitely many nonzero coefficients, so there's no polynomial with all equal to one. – user2345215 Nov 22 '14 at 15:51
• Generating funtion for integers in binary?! – Winther Nov 22 '14 at 15:58

It's called a polynomial with $0$, $1$ coefficients, or a polynomial with coefficients from $\{0,1\}$.
A polynomial with all coefficients equal to $1$ would be of the form $1+x+x^2+\cdots+x^{n-1}+x^n$.