CoCalc -- SU_degeneracy.py

GitHub Repository: GuillaumeLaplante-Anfossi/Poissons
Path: blob/main/GeneratingDiagonalsViaShift/SU_degeneracy.py
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'''
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SU degeneracy projections, 
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using Proposition 6 of DIAGONALS ON THE PERMUTAHEDRA, MULTIPLIHEDRA AND ASSOCIAHEDRA.
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'''
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from itertools import combinations
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from diagonals_via_shift import SU_diag, LA_diag
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def exceptional(A,k):
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    '''
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    return: True if the subset A_k is exceptional, False if not
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    '''
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    minAk = min(A[k])
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    maxAk = max(A[k])
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    for x in A[k+1:]:
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        for aij in x:
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            if minAk < aij and aij < maxAk:
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                return True
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    return False
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def Mult_filter(A):
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    for j in range(len(A)-1):
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        minAj = min(A[j])
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        if (min(A[j]) > min([min(x) for x in A[j+1:]])) and exceptional(A,j):
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            return False
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    return True
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def LA_Mult_diag(n):
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    valid = []
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    for p in LA_diag(n):
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        if Mult_filter(p[0]) and Mult_filter(p[1]):
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            valid.append(p)
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    return valid
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def SU_Mult_diag(n):
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    valid = []
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    for p in SU_diag(n):
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        if Mult_filter(p[0]) and Mult_filter(p[1]):
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            valid.append(p)
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    return valid
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def Assoc_filter(A):
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    for k in range(len(A)-1):
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        if exceptional(A,k):
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            return False
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    return True
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def LA_Assoc_diag(n):
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    valid = []
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    for p in LA_diag(n):
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        if Assoc_filter(p[0]) and Assoc_filter(p[1]):
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            valid.append(p)
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    return valid
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def SU_Assoc_diag(n):
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    valid = []
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    for p in SU_diag(n):
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        if Assoc_filter(p[0]) and Assoc_filter(p[1]):
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            valid.append(p)
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    return valid
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def compare_Mult(n):
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    LA = sorted(LA_Mult_diag(n))
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    SU = sorted(SU_Mult_diag(n))
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    LA_only = []
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    SU_only = []
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    shared = []
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    for x in LA:
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        if x in SU:
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            shared.append(x)
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        else:
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            LA_only.append(x)
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    for x in SU:
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        if x not in LA:
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            SU_only.append(x)
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    return LA, LA_only, shared, SU_only, SU
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def compare_Assoc(n):
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    LA = sorted(LA_Assoc_diag(n))
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    SU = sorted(SU_Assoc_diag(n))
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    LA_only = []
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    SU_only = []
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    shared = []
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    for x in LA:
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        if x in SU:
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            shared.append(x)
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        else:
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            LA_only.append(x)
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    for x in SU:
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        if x not in LA:
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            SU_only.append(x)
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    return LA, LA_only, shared, SU_only, SU
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def iso2(p,n):
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    '''
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    Applies the iso t(r x r)
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    '''
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    def r(op,n):
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        rev = []
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        for block in op:
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            revblock = []
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            for x in block:
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                revblock.append(n-x+1)
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            rev.append(sorted(revblock))
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        return rev
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def iso1(p):
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    '''
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    Applies the iso t(s x s)
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    '''
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    return [p[1][::-1],p[0][::-1]]
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if __name__ == '__main__':
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    print("\nAssoc")
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    for n in range(1,6):
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        print("\nn={}".format(n))
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        LA, LA_only, shared, SU_only, SU = compare_Assoc(n)
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        print("|LA|={}, |LA only|={}, |shared|={}, |SU only|={}, |SU|={}".format(
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            len(LA), len(LA_only), len(shared), len(SU_only), len(SU)))
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    print("\nMult")
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    for n in range(1,8):
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        print("\nn={}".format(n))
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        LA, LA_only, shared, SU_only, SU = compare_Mult(n)
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        print("|LA|={}, |LA only|={}, |shared|={}, |SU only|={}, |SU|={}".format(
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            len(LA), len(LA_only), len(shared), len(SU_only), len(SU)))
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