BPS States, Crystals, and Matrices

<table>Infinite pyramids with one and four balls in the top row, with generating functions given, respectively, by <svg height="21.6625" id="M174" style="vertical-align:-4.85281pt" version="1.1" viewbox="0 0 50.275002 21.6625" width="50.275002" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑍</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">p</tspan>
<tspan style="font-size: 8.75px; " x="4.3147359" y="0">y</tspan>
<tspan style="font-size: 8.75px; " x="8.6907358" y="0">r</tspan>
<tspan style="font-size: 8.75px; " x="11.587648" y="0">a</tspan>
<tspan style="font-size: 8.75px; " x="15.473536" y="0">m</tspan>
<tspan style="font-size: 8.75px; " x="22.282593" y="0">i</tspan>
<tspan style="font-size: 8.75px; " x="24.715649" y="0">d</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.3,54.85)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
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</svg> and <svg height="21.6625" id="M175" style="vertical-align:-4.85281pt" version="1.1" viewbox="0 0 50.275002 21.6625" width="50.275002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.6625)">
<g transform="translate(72,-54.67)">
<text transform="matrix(1,0,0,-1,-71.95,59.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑍</tspan>
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<text transform="matrix(1,0,0,-1,-61.42,65.97)">
<tspan style="font-size: 8.75px; " x="0" y="0">p</tspan>
<tspan style="font-size: 8.75px; " x="4.3147359" y="0">y</tspan>
<tspan style="font-size: 8.75px; " x="8.6907358" y="0">r</tspan>
<tspan style="font-size: 8.75px; " x="11.587648" y="0">a</tspan>
<tspan style="font-size: 8.75px; " x="15.473536" y="0">m</tspan>
<tspan style="font-size: 8.75px; " x="22.282593" y="0">i</tspan>
<tspan style="font-size: 8.75px; " x="24.715649" y="0">d</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.3,54.85)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
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</svg>.</table>

Advances in High Energy Physics

BPS States, Crystals, and Matrices

Figure 2