Permutation-partition pairs. II. Bounds on the genus of the amalgamation of graphs
Permutation-partition pairs. II. Bounds on the genus of the amalgamation of graphs
Bounds are derived on the extent to which the parameter <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu left-parenthesis upper P comma product right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>μ<!-- μ --></mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>P</mml:mi> <mml:mo>,</mml:mo> <mml:mspace width="thinmathspace" /> <mml:mo>∏<!-- ∏ --></mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mu (P,\,\prod )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can fail to be …