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Posets :: areIsomorphic

areIsomorphic -- determines if two posets are isomorphic

Synopsis

Description

Two posets are isomorphic if there is a partial order preserving bijection between the ground sets of the posets which preserves the specified ground set partitions.

If mu and nu are not specified, then the trivial partitions (the entire ground set in a single part) are used.
i1 : C = chain 5;
i2 : P = poset {{a,b},{b,c},{c,d},{d,e}};
i3 : areIsomorphic(C, P)

o3 = true
The product of n chains of length 2 is isomorphic to the boolean lattice on n elements. These are also isomorphic to the divisor lattice on the product of n distinct primes.
i4 : B = booleanLattice 5;
i5 : B == product(5, i -> chain 2)

o5 = true
i6 : B == divisorPoset (2*3*5*7*11)

o6 = true
i7 : B == divisorPoset (2^2*3*5*7)

o7 = false
This method uses the method isomorphism, which was ported from John Stembridge’s Maple package available at http://www.math.lsa.umich.edu/~jrs/maple.html#posets.

See also

Ways to use areIsomorphic :