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How to plot lattice paths ?

asked 2015-12-29 02:30:07 -0600

hans gravatar image

updated 2015-12-30 12:31:57 -0600

I have seen that the command

for D in DyckWords(n):
    D.pretty_print(type="NE-SE")

gives a nice plot of all Dyck paths.

Is there an analogous command for the set of all 2^n lattice paths of length n with up- and downsteps of height 1? Please give details, I am a newcomer to Sage.

Edit: Sorry if my question is not properly formulated. Perhaps I should modify my question somewhat: The command

D = DyckWords(6)[3]
D.pretty_print(type="NE-SE")

gives a nice picture (which I unfortunately cannot copy) of the Dyckpath corresponding to [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0] by interpreting 0 with a down-step and 1 with an up-step.

How can I print a corresponding picture for a word which corresponds to a path with negative values?

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answered 2015-12-30 14:23:21 -0600

Here is how you could explore this question.

sage: DD = DyckWords(11)
sage: D = DD.an_element()
sage: D
[1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]
sage: D.pretty_print(type="NE-SE")
/\/\/\/\/\/\/\/\/\/\/\

Documentation:

sage: D.pretty_print?

Source code:

sage: D.pretty_print??

We see that the source code calls self._repr_lattice() so we check out the documentation for this method:

sage: D._repr_lattice?

and the source code:

sage: D._repr_lattice??

and check if we can adapt it to other lattice paths.

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Asked: 2015-12-29 02:30:07 -0600

Seen: 117 times

Last updated: Dec 30 '15