The command AreIsomorphic(P1,P2) checks whether the partially ordered sets P1 and P2 are isomorphic or not. To be more precise, let us denote by V1 (resp. V2) the underlying set of P1 (resp. P2) and  by R1 (resp. R2 ) the binary relation on V defining P1 (resp. P2). The posets P1 and P2 are isomorphic whenever there exists a one-to-one map f from V1  to V2 and for any two elements a and b in V1,  R1(a,b) holds if and only if R2(f(a),f(b)) holds.

$\mathrm{with}\left(\mathrm{PartiallyOrderedSets}\right)\:$

$\mathrm{leq}≔\mathrm{`<=`}\&colon;$

$\mathrm{lneq}≔\mathrm{`<`}\&colon;$

$U≔\left\{1\&comma;2\&comma;3\right\}\&colon;$

$\mathrm{poset3}≔\mathrm{PartiallyOrderedSet}\left(U\&comma;\mathrm{leq}\&comma;\mathrm{reflexive}=\mathrm{checktrue}\right)$

$\mathrm{poset3}≔\mathrm{<\; a\; poset\; with\; 3\; elements\; >}$

$\mathrm{DrawGraph}\left(\mathrm{poset3}\right)$

$\mathrm{poset3\_1}≔\mathrm{PartiallyOrderedSet}\left(U\&comma;\mathrm{lneq}\&comma;\mathrm{reflexive}=\mathrm{useclosure}\right)$

$\mathrm{poset3\_1}≔\mathrm{<\; a\; poset\; with\; 3\; elements\; >}$

$\mathrm{DrawGraph}\left(\mathrm{poset3\_1}\right)$

$\mathrm{AreEqual}\left(\mathrm{poset3}\&comma;\mathrm{poset3\_1}\right)\&semi;$$\mathrm{AreIsomorphic}\left(\mathrm{poset3}\&comma;\mathrm{poset3\_1}\right)$

$\mathrm{true}$

$\mathrm{true}$

$X≔\left\{4\&comma;5\&comma;6\right\}\&colon;$$\mathrm{poset3\_2}≔\mathrm{PartiallyOrderedSet}\left(X\&comma;\mathrm{leq}\&comma;\mathrm{reflexive}=\mathrm{checktrue}\right)$

$\mathrm{poset3\_2}≔\mathrm{<\; a\; poset\; with\; 3\; elements\; >}$

$\mathrm{DrawGraph}\left(\mathrm{poset3\_2}\right)$

$\mathrm{AreEqual}\left(\mathrm{poset3}\&comma;\mathrm{poset3\_2}\right)\&semi;$$\mathrm{AreIsomorphic}\left(\mathrm{poset3}\&comma;\mathrm{poset3\_2}\right)$

$\mathrm{false}$

$\mathrm{true}$

$G≔\mathrm{GraphTheory}:-\mathrm{Graph}\left(\mathrm{directed}\&comma;\left[1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\right]\&comma;\left\{\left[1\&comma;1\right]\&comma;\left[1\&comma;2\right]\&comma;\left[1\&comma;3\right]\&comma;\left[1\&comma;4\right]\&comma;\left[1\&comma;5\right]\&comma;\left[1\&comma;6\right]\&comma;\left[2\&comma;2\right]\&comma;\left[2\&comma;4\right]\&comma;\left[2\&comma;6\right]\&comma;\left[3\&comma;3\right]\&comma;\left[3\&comma;5\right]\&comma;\left[3\&comma;6\right]\&comma;\left[4\&comma;4\right]\&comma;\left[4\&comma;6\right]\&comma;\left[5\&comma;5\right]\&comma;\left[5\&comma;6\right]\&comma;\left[6\&comma;6\right]\right\}\right)$

$G≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 6\; vertices,\; 11\; arcs,\; and\; 6\; self-loops}$

$\mathrm{poset6}≔\mathrm{PartiallyOrderedSet}\left(G\right)$

$\mathrm{poset6}≔\mathrm{<\; a\; poset\; with\; 6\; elements\; >}$

$\mathrm{DrawGraph}\left(\mathrm{poset6}\right)$

$\mathrm{poset8}≔\mathrm{PartiallyOrderedSet}\left(\left[1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\right]\&comma;\mathrm{Array}\left(\left[\left\{1\&comma;2\&comma;3\right\}\&comma;\left\{2\&comma;4\right\}\&comma;\left\{3\&comma;5\right\}\&comma;\left\{4\&comma;6\right\}\&comma;\left\{5\&comma;6\right\}\&comma;\left\{6\right\}\right]\right)\&comma;\mathrm{input}=\mathrm{transitivereduction}\right)$

$\mathrm{poset8}≔\mathrm{<\; a\; poset\; with\; 6\; elements\; >}$

$\mathrm{DrawGraph}\left(\mathrm{poset8}\right)$

$\mathrm{AreEqual}\left(\mathrm{poset6}\&comma;\mathrm{poset8}\right)\&semi;$$\mathrm{AreIsomorphic}\left(\mathrm{poset6}\&comma;\mathrm{poset8}\right)$

$\mathrm{true}$

$\mathrm{true}$

Richard P. Stanley: Enumerative Combinatorics 1. 1997, Cambridge Studies in Advanced Mathematics. Vol. 49. Cambridge University Press.

The PartiallyOrderedSets[AreIsomorphic] command was introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.