A Pascal-like Bound for the Number of Necklaces with Fixed Density

Abstract

A bound resembling Pascal's identity is presented for binary necklaces with fixed density using Lyndon words with fixed density. The result is generalized to k-ary necklaces and Lyndon words with fixed content. The bound arises in the study of Nichols algebras of diagonal type.

6 pages, Lyndon words, necklaces, Nichols algebras