A bound for decompositions of $m$-convex sets whose LNC points lie in a hyperplane
A bound for decompositions of $m$-convex sets whose LNC points lie in a hyperplane
A set <italic>S</italic> in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Superscript d"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>d</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{R^d}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is said to be <italic>m</italic>-convex, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m greater-than-or-slanted-equals 2"> <mml:semantics> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>⩾<!-- ⩾ --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">m \geqslant 2</mml:annotation> </mml:semantics> …