Geometric Realization of Some Triangle-Free Combinatorial Configurations <svg style="vertical-align:-3.25793pt;width:21.85px;" id="M1" height="14.9375" version="1.1" viewBox="0 0 21.85 14.9375" width="21.85"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,14.9375)">
		<g transform="translate(72,-60.05)">
			<text transform="matrix(1,0,0,-1,-71.95,63.35)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝟐</tspan>
				<tspan style="font-size: 12.50px; " x="6.2515001" y="0">𝟐</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-59.45,60.22)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝟑</tspan>
			</text>

		</g>
	</g>
</svg>

<table>The configuration 11#(4,2;3) labeled as explained in the text. The parameter <svg height="14.75" id="M44" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 106.5125 14.75" width="106.5125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.75)">
<g transform="translate(72,-60.2)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="20.604944" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="23.105543" y="0">𝑄</tspan>
</text>
<text transform="matrix(1,0,0,-1,-39.07,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-34.2,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-26.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑏</tspan>
</text>
<text transform="matrix(1,0,0,-1,-22.16,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="5.9764342" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="8.4770336" y="0">𝑃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-6.26,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-1.38,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
</text>
<text transform="matrix(1,0,0,-1,6.05,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑏</tspan>
</text>
<text transform="matrix(1,0,0,-1,10.66,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">|</tspan>
</text>
</g>
</g>
</svg>  equals 0.188459 for this configuration.</table>

International Scholarly Research Notices

fig1

Figure 1

Figure 1: Geometric Realization of Some Triangle-Free Combinatorial Configurations <svg style="vertical-align:-3.25793pt;width:21.85px;" id="M1" height="14.9375" version="1.1" viewBox="0 0 21.85 14.9375" width="21.85"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,14.9375)">
		<g transform="translate(72,-60.05)">
			<text transform="matrix(1,0,0,-1,-71.95,63.35)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝟐</tspan>
				<tspan style="font-size: 12.50px; " x="6.2515001" y="0">𝟐</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-59.45,60.22)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝟑</tspan>
			</text>

		</g>
	</g>
</svg> 

International Scholarly Research Notices

Geometric Realization of Some Triangle-Free Combinatorial Configurations 𝟐 𝟐 𝟑

Figure 1

Geometric Realization of Some Triangle-Free Combinatorial Configurations