$n$-Colour self-inverse compositions

Composition inverses of the variations of the Baum-Sweet sequence

Studying and comparing arithmetic properties of a given automatic sequence and the sequence of coefficients of the composition inverse of the associated formal power series (the formal inverse of that sequence) is an interesting problem. This problem was studied before for the Thue-Morse sequence. In this paper, we study arithmetic properties of the formal inverses of two sequences closely related to the well-known Baum-Sweet sequence. We give the recurrence relations for their formal inverses and we determine whether the sequences of indices at which these formal inverses take value $0$ and $…

通过将秩降低一得到的辛列的逆约化映射

The inverse reduction map of a symplectic column by decreasing the rank by one

研究辛列的逆约化映射，利用之前给出的因式分解及渡边对约化映射的写法，通过检测秩降一的辛列，避免映射复合，写出辛列上约化映射的逆。

Some convolution identities and an inverse relation involving partial Bell polynomials

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting multinomial formula for the binomial coefficients. The inverse relation is deduced from a parametrization of suitable identities that facilitate dealing with compositions of Bell polynomials.

Logarithmic form of Lagrange inversion formula

We give presentation of composition inverse of formal power serie in a logarithmic form.