- FindStat

Identifier

St001591: Integer compositions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,1]=>1
[2]=>1
[1,1,1]=>1
[1,2]=>1
[2,1]=>1
[3]=>1
[1,1,1,1]=>2
[1,1,2]=>1
[1,2,1]=>2
[1,3]=>1
[2,1,1]=>1
[2,2]=>2
[3,1]=>1
[4]=>1
[1,1,1,1,1]=>10
[1,1,1,2]=>3
[1,1,2,1]=>2
[1,1,3]=>1
[1,2,1,1]=>2
[1,2,2]=>2
[1,3,1]=>1
[1,4]=>1
[2,1,1,1]=>1
[2,1,2]=>2
[2,2,1]=>3
[2,3]=>2
[3,1,1]=>1
[3,2]=>1
[4,1]=>1
[5]=>1
[1,1,1,1,1,1]=>53
[1,1,1,1,2]=>11
[1,1,1,2,1]=>1
[1,1,1,3]=>3
[1,1,2,1,1]=>13
[1,1,2,2]=>3
[1,1,3,1]=>3
[1,1,4]=>1
[1,2,1,1,1]=>13
[1,2,1,2]=>3
[1,2,2,1]=>6
[1,2,3]=>2
[1,3,1,1]=>4
[1,3,2]=>2
[1,4,1]=>2
[1,5]=>1
[2,1,1,1,1]=>3
[2,1,1,2]=>1
[2,1,2,1]=>4
[2,1,3]=>2
[2,2,1,1]=>3
[2,2,2]=>5
[2,3,1]=>2
[2,4]=>2
[3,1,1,1]=>1
[3,1,2]=>3
[3,2,1]=>2
[3,3]=>2
[4,1,1]=>1
[4,2]=>2
[5,1]=>1
[6]=>1
[1,1,1,1,1,1,1]=>589
[1,1,1,1,1,2]=>61
[1,1,1,1,2,1]=>4
[1,1,1,1,3]=>11
[1,1,1,2,1,1]=>53
[1,1,1,2,2]=>3
[1,1,1,3,1]=>3
[1,1,1,4]=>3
[1,1,2,1,1,1]=>42
[1,1,2,1,2]=>16
[1,1,2,2,1]=>5
[1,1,2,3]=>3
[1,1,3,1,1]=>9
[1,1,3,2]=>6
[1,1,4,1]=>2
[1,1,5]=>1
[1,2,1,1,1,1]=>40
[1,2,1,1,2]=>16
[1,2,1,2,1]=>16
[1,2,1,3]=>4
[1,2,2,1,1]=>9
[1,2,2,2]=>9
[1,2,3,1]=>3
[1,2,4]=>2
[1,3,1,1,1]=>10
[1,3,1,2]=>5
[1,3,2,1]=>3
[1,3,3]=>2
[1,4,1,1]=>2
[1,4,2]=>2
[1,5,1]=>1
[1,6]=>1
[2,1,1,1,1,1]=>11
[2,1,1,1,2]=>4
[2,1,1,2,1]=>3
[2,1,1,3]=>1
[2,1,2,1,1]=>14
[2,1,2,2]=>6
[2,1,3,1]=>3
[2,1,4]=>2
[2,2,1,1,1]=>3
[2,2,1,2]=>5
[2,2,2,1]=>8
[2,2,3]=>6
[2,3,1,1]=>2
[2,3,2]=>3
[2,4,1]=>2
[2,5]=>2
[3,1,1,1,1]=>3
[3,1,1,2]=>3
[3,1,2,1]=>2
[3,1,3]=>3
[3,2,1,1]=>2
[3,2,2]=>3
[3,3,1]=>4
[3,4]=>2
[4,1,1,1]=>1
[4,1,2]=>2
[4,2,1]=>2
[4,3]=>2
[5,1,1]=>1
[5,2]=>1
[6,1]=>1
[7]=>1
                    

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Description

The number of graphs with the given composition of multiplicities of Laplacian eigenvalues.

Code

def mapping(G):
    if G.num_verts() > 30:
        raise ValueError("Graph too big for this map")
    s = G.spectrum(laplacian=True)
    c = []
    i, o = 0, None
    for v in s:
        if v != o:
            c.append(i)
            i, o = 0, v
        i += 1
    c.append(i)
    return Composition(c[1:])
@cached_function
def preimages(level):
    print("computing preimages for level", level)
    result = dict()
    for el in graphs(level):
        image = mapping(el)
        result[image] = result.get(image, 0) + 1
    return result

def statistic(x):
    return preimages(x.size()).get(x, 0)

Created

Sep 12, 2020 at 09:17 by Martin Rubey

Updated

Sep 12, 2020 at 09:17 by Martin Rubey