Abstract
We discuss a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. We give several equivalent descriptions, and prove some algebraic and combinatorial properties. In addition, we characterize shuffles in terms of open sets in a topological space associated to a pair of trees. Our notion of shuffle is motivated by the theory of operads and occurs in the theory of dendroidal sets, but our presentation is independent and entirely self-contained.
| Original language | English |
|---|---|
| Pages (from-to) | 55-72 |
| Number of pages | 18 |
| Journal | European Journal of Combinatorics |
| Volume | 71 |
| DOIs | |
| Publication status | Published - 1 Jun 2018 |
Funding
We would like to thank James Cranch who wrote a computer program enumerating shuffles of some small trees, which led to Examples 3.4 and 3.6 in the paper. The first author is also indebted to Denis-Charles Cisinski and Gijs Heuts for discussions which improved his understanding of shuffles. We also like to thank our home universities and NWO for supporting our mutual visits. Finally, we would like to thank the referees for their careful comments on an earlier version of this paper. The first author is partially funded by the ANR grants ANR-13-BS02-0005-02 CATHRE and ANR-16-CE40-0003 ChroK .