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When I input the Bruhat poset of type Bn in Sage as follows

W = WeylGroup("B2", prefix="s") 
P = W.bruhat_poset() 
display(plot(P))

the elements look like s2s1s2.

Question: Is there a way to represent the element in the form of signed permutation as for example findstat does (see for example http://www.findstat.org/StatisticsDatabase/St001427/ ) so that one sees the signed permutation in the graph as for example -132 or -3-21. (The motivation is that one can use the code in the thread https://ask.sagemath.org/question/56230/obtaining-incidence-algebras-for-gap-via-sage/ to obtain the quiver algebra in GAP with names one can regognize later).

Thanks for any help

When I input the Bruhat poset of type Bn in Sage as follows

W = WeylGroup("B2", prefix="s") 
P = W.bruhat_poset() 
display(plot(P))

the elements look like s2s1s2.s2*s1*s2.

Question: Is there a way to represent the element in the form of signed permutation as for example findstat does (see for example http://www.findstat.org/StatisticsDatabase/St001427/ ) so that one sees the signed permutation in the graph as for example -132 or -3-21. (The motivation is that one can use the code in the thread https://ask.sagemath.org/question/56230/obtaining-incidence-algebras-for-gap-via-sage/ to obtain the quiver algebra in GAP with names one can regognize later).

Thanks for any help

When I input the Bruhat poset of type Bn in Sage as follows

W = WeylGroup("B2", prefix="s") 
P = W.bruhat_poset() 
display(plot(P))

the elements look like s2*s1*s2.

Question: Is there a way to represent (in the picture of the poset in Sage) the element in the form of signed permutation as for example findstat does (see for example http://www.findstat.org/StatisticsDatabase/St001427/ ) but so that one sees the signed permutation in the graph as - is replaced by 0 and brackets and commas are ommited? So for example -132 or -3-21. all signed permutations for $n=2$ would look as follows in this notation:

12
102
012
0102
21
201
021
0201

(The motivation is that one can use the code in the thread https://ask.sagemath.org/question/56230/obtaining-incidence-algebras-for-gap-via-sage/ to obtain the quiver algebra in GAP with names one can regognize later).

Thanks for any help

(I edited the question, to make it more clear)

When I input the Bruhat poset of type Bn in Sage as follows

W = WeylGroup("B2", prefix="s") 
P = W.bruhat_poset() 
display(plot(P))

the elements look like s2*s1*s2.

Question: Is there a way to represent (in the picture of the poset in Sage) the element elements in the form of signed permutation as for example findstat does (see for example http://www.findstat.org/StatisticsDatabase/St001427/ ) but so that - is replaced by 0 and brackets and commas are ommited? So for example all signed permutations for $n=2$ would look as follows in this notation:

12
102
012
0102
21
201
021
0201

(The motivation is that one can use the code in the thread https://ask.sagemath.org/question/56230/obtaining-incidence-algebras-for-gap-via-sage/ to obtain the quiver algebra in GAP with names one can regognize later).

Thanks for any help