# Seven Trees in One

- Published in 1994
- Added on

In the collections

Following a remark of Lawvere, we explicitly exhibit a particularly elementary bijection between the set T of finite binary trees and the set T^7 of seven-tuples of such trees. "Particularly elementary" means that the application of the bijection to a seven-tuple of trees involves case distinctions only down to a fixed depth (namely four) in the given seven-tuple. We clarify how this and similar bijections are related to the free commutative semiring on one generator X subject to X=1+X^2. Finally, our main theorem is that the existence of particularly elementary bijections can be deduced from the provable existence, in intuitionistic type theory, of any bijections at all.

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- key
- SevenTreesinOne
- type
- article
- date_added
- 2018-11-26
- date_published
- 1994-09-29

### BibTeX entry

@article{SevenTreesinOne, key = {SevenTreesinOne}, type = {article}, title = {Seven Trees in One}, author = {Andreas Blass}, abstract = {Following a remark of Lawvere, we explicitly exhibit a particularly elementary bijection between the set T of finite binary trees and the set T^7 of seven-tuples of such trees. "Particularly elementary" means that the application of the bijection to a seven-tuple of trees involves case distinctions only down to a fixed depth (namely four) in the given seven-tuple. We clarify how this and similar bijections are related to the free commutative semiring on one generator X subject to X=1+X^2. Finally, our main theorem is that the existence of particularly elementary bijections can be deduced from the provable existence, in intuitionistic type theory, of any bijections at all.}, comment = {}, date_added = {2018-11-26}, date_published = {1994-09-29}, urls = {http://arxiv.org/abs/math/9405205v1,http://arxiv.org/pdf/math/9405205v1}, collections = {Fun maths facts,Unusual arithmetic}, url = {http://arxiv.org/abs/math/9405205v1 http://arxiv.org/pdf/math/9405205v1}, year = 1994, urldate = {2018-11-26}, archivePrefix = {arXiv}, eprint = {math/9405205}, primaryClass = {math.LO} }