Séminaire Lotharingien de Combinatoire, B78a (2018), 46 pp.
Gilbert Labelle
Binomial Species and Combinatorial Exponentiation
Abstract.
We introduce a "binomial" species, B(X,Y)=(1+X)îY
= E(Y Lg(1+X)), where E(X)
is the species of finite sets and Lg(1+X) is
the combinatorial logarithm. The expansion of B includes, by
specialization of variables, the classical binomial expansion,
binomial expansions for symmetric functions, and (q,t)-series. We
also define and study a new exponentiation operation, F\,îG,
between species.
Received: April 14, 2016.
Revised: March 31, 2017, June 22, 2017.
Accepted: July 24, 2017.
The following versions are available: