Is there an algorithmic way to map the natural numbers to unique k-ary trees?


I am familiar with the work of Tychonievich who created a mapping from integers to binary trees. <https://www.cs.virginia.edu/~lat7h/blog/posts/434.html>


Is there something similar for k-ary trees?



mapping integers to k-ary trees
If you search for "ranking $k$-ary trees" or "ranking $t$-ary trees" you will find several published papers on this. For example:


[This](https://epubs.siam.org/doi/abs/10.1137/0207039?casa_token=L7KsyEFGnGMAAAAA%3AtRJdKQBkcAnPHnV1GQaFhmsMHA1znPEnW942T513tvnhIhfLFposVAp5vi_XK2JmlbSVWBGlDKeS&)


[This](https://epubs.siam.org/doi/abs/10.1137/0207034?casa_token=BRMD50DToJsAAAAA:3HA_MEs4gzr_HGo0uCkqtdIZGD4OzkskBQfPqL7TOg8RQ33coSr4yj1ye8owuRGoacD6r5kXZ938)


