Partition regularity of polynomial systems near zero
Partition regularity of polynomial systems near zero
Abstract Recently, S. Kanti Patra and Md. Moid Shaikh proved the existence of monochromatic solutions to systems of polynomial equations near zero for particular dense subsemigroups $$(S,+)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>S</mml:mi> <mml:mo>,</mml:mo> <mml:mo>+</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> of $$(\mathbb {R}^{+},+)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> …