An Application of Iterative Pushdown Automata  to Contour Words of Balls and Truncated Balls in Hyperbolic Tessellations

<table>The representation of <svg height="14.625" id="M205" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 28.525 14.625" width="28.525" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.625)">
<g transform="translate(72,-60.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜕</tspan>
<tspan style="font-size: 12.50px; " x="6.3765302" y="0">𝑊</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.11,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
</g>
</g>
</svg>. (a) the pentagrid. (b) the heptagrid. In both cases, the contour word is <svg height="10.7375" id="M206" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 116.6125 10.7375" width="116.6125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.7375)">
<g transform="translate(72,-63.41)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
<tspan style="font-size: 12.50px; " x="5.1012239" y="0">𝑠</tspan>
<tspan style="font-size: 12.50px; " x="10.602544" y="0">𝑠</tspan>
<tspan style="font-size: 12.50px; " x="16.103865" y="0">𝑏</tspan>
<tspan style="font-size: 12.50px; " x="21.980274" y="0">𝑤</tspan>
<tspan style="font-size: 12.50px; " x="31.670099" y="0">𝑏</tspan>
<tspan style="font-size: 12.50px; " x="37.546509" y="0">𝑤</tspan>
<tspan style="font-size: 12.50px; " x="47.236336" y="0">𝑤</tspan>
<tspan style="font-size: 12.50px; " x="56.926159" y="0">𝑏</tspan>
<tspan style="font-size: 12.50px; " x="62.80257" y="0">𝑤</tspan>
<tspan style="font-size: 12.50px; " x="72.492393" y="0">𝑤</tspan>
<tspan style="font-size: 12.50px; " x="82.18222" y="0">𝑠</tspan>
<tspan style="font-size: 12.50px; " x="87.68354" y="0">𝑠</tspan>
</text>
</g>
</g>
</svg>.</table>

International Scholarly Research Notices

fig5

Figure 5

Figure 5: An Application of Iterative Pushdown Automata  to Contour Words of Balls and Truncated Balls in Hyperbolic Tessellations 