Add to ORKGAbstract. For each natural number n, we characterise the invertible series (under composition) that are the composition of n proper involutions. We work with formal power series in one variable over a field of characteristic zero. We also describe the reversible series (those conjugate to their own inverses), and the series that are the composition of n reversible series
A pair of simple bivariate inverse series relations are used by embedding machinery to produce seve...
We use sums over integer compositions analogous to generating functions in partition theory, to expr...
AbstractWe prove that all and only the invertible one-variable partial recursive dunctions can be ge...
For each natural number n, we characterise the invertible series (under composition) that are the c...
An explicit method for finding every coefficient of the reversed series of a power series in one var...
The classical algorithms require order n 3 operations to compute the first n terms in the reversion ...
An element g of a group is called reversible if it is conjugate in the group to its inverse. An ele...
AbstractAn algorithm that yields every coefficient of the reversed series of a formal power series i...
We deepen here the insight on formal power series. We temporarily abandon formality and consider the...
This paper deals with the composition of normalised formal power series, in one variable, over an ar...
Fa\`a di Bruno's formula gives an expression for the derivatives of the composition of two real-valu...
Let F(x) = f1x + f2(x)(x) + . . . be a formal power series over a field Delta. Let F superscript 0(x...
AbstractThis paper presents a combinatorial theory of formal power series. The combinatorial interpr...
AbstractWe explain the construction of fields of formal infinite series in several variables, genera...
The theory of arithmetic functions and the theory of formal power series are classical and active pa...
A pair of simple bivariate inverse series relations are used by embedding machinery to produce seve...
We use sums over integer compositions analogous to generating functions in partition theory, to expr...
AbstractWe prove that all and only the invertible one-variable partial recursive dunctions can be ge...
For each natural number n, we characterise the invertible series (under composition) that are the c...
An explicit method for finding every coefficient of the reversed series of a power series in one var...
The classical algorithms require order n 3 operations to compute the first n terms in the reversion ...
An element g of a group is called reversible if it is conjugate in the group to its inverse. An ele...
AbstractAn algorithm that yields every coefficient of the reversed series of a formal power series i...
We deepen here the insight on formal power series. We temporarily abandon formality and consider the...
This paper deals with the composition of normalised formal power series, in one variable, over an ar...
Fa\`a di Bruno's formula gives an expression for the derivatives of the composition of two real-valu...
Let F(x) = f1x + f2(x)(x) + . . . be a formal power series over a field Delta. Let F superscript 0(x...
AbstractThis paper presents a combinatorial theory of formal power series. The combinatorial interpr...
AbstractWe explain the construction of fields of formal infinite series in several variables, genera...
The theory of arithmetic functions and the theory of formal power series are classical and active pa...
A pair of simple bivariate inverse series relations are used by embedding machinery to produce seve...
We use sums over integer compositions analogous to generating functions in partition theory, to expr...
AbstractWe prove that all and only the invertible one-variable partial recursive dunctions can be ge...