BPS States, Crystals, and Matrices

<table>Conifold crystal in the chamber with positive <svg height="10.325" id="M553" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑅</tspan>
</text>
</g>
</g>
</svg> and <svg height="11.0625" id="M554" style="vertical-align:-0.30096pt" version="1.1" viewbox="0 0 65.412498 11.0625" width="65.412498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">&lt;</tspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">𝐵</tspan>
<tspan style="font-size: 12.50px; " x="33.933144" y="0">&lt;</tspan>
<tspan style="font-size: 12.50px; " x="45.97353" y="0">3</tspan>
</text>
</g>
</g>
</svg> takes form of pyramid partitions with 3 stones in the top row. Its generating function is given by <svg height="21.3375" id="M555" style="vertical-align:-4.68874pt" version="1.1" viewbox="0 0 144 21.3375" width="144" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.3375)">
<g transform="translate(72,-54.93)">
<text transform="matrix(1,0,0,-1,-71.95,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑍</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.3,56.53)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">|</tspan>
<tspan style="font-size: 8.75px; " x="6.1264" y="0">1</tspan>
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<text transform="matrix(1,0,0,-1,-47.82,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">⟨</tspan>
<tspan style="font-size: 12.50px; " x="17.029085" y="0">Ω</tspan>
</text>
<text transform="matrix(1,0,0,-1,-21.48,56.53)">
<tspan style="font-size: 8.75px; " x="0" y="0">+</tspan>
</text>
<text transform="matrix(1,0,0,-1,-14.99,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">(</tspan>
</text>
<g>
<path d="m -8.33,70.71 14.27,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-8.33,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑊</tspan>
</text>
<text transform="matrix(1,0,0,-1,5.94,56.53)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,10.82,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">)</tspan>
</text>
<text transform="matrix(1,0,0,-1,14.98,64.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,19.85,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">Ω</tspan>
</text>
<text transform="matrix(1,0,0,-1,31.66,56.53)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
</text>
<text transform="matrix(1,0,0,-1,38.15,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">⟩</tspan>
</text>
</g>
</g>
</svg>.</table>

Advances in High Energy Physics

BPS States, Crystals, and Matrices

Figure 13