Prismatic Sets Associated with Planar Rooted Trees

<p>A general planar rooted tree of the form <svg height="14.7207pt" id="M94" style="vertical-align:-6.90688pt" version="1.1" viewbox="-0.0498162 -7.81382 70.2229 14.7207" width="70.2229pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.368,3.132)"><path d="M481 430L460 436C440 442 393 451 366 451C348 451 325 448 313 446C267 437 195 409 147 367C79 308 24 211 24 105C24 37 56 -12 93 -12C121 -12 156 1 199 32C246 66 313 122 349 168H351L286 -147C274 -205 261 -215 210 -224L199 -226L193 -255L438 -243L442 -214L417 -212C364 -208 359 -200 370 -140L433 204C455 324 469 389 481 430ZM391 385C382 336 366 260 358 238C321 178 209 59 143 59C129 59 115 83 115 131C115 207 152 317 220 373C243 392 282 403 314 403C348 403 374 395 391 385Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,8.863,5.233)"><path d="M455 312C455 472 400 635 248 635C95 635 39 458 39 312C39 144 93 -12 248 -12C400 -12 455 166 455 312ZM361 314C361 173 337 30 249 30C163 30 131 174 131 313C131 451 155 594 248 594C334 594 361 454 361 314Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.005,0)"><path d="M574 548H512L295 69H293L76 548H14L263 0H325L574 548Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.542,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.685,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.828,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.731,0)"><path d="M574 548H512L295 69H293L76 548H14L263 0H325L574 548Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.267,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,57.635,3.132)"><path d="M481 430L460 436C440 442 393 451 366 451C348 451 325 448 313 446C267 437 195 409 147 367C79 308 24 211 24 105C24 37 56 -12 93 -12C121 -12 156 1 199 32C246 66 313 122 349 168H351L286 -147C274 -205 261 -215 210 -224L199 -226L193 -255L438 -243L442 -214L417 -212C364 -208 359 -200 370 -140L433 204C455 324 469 389 481 430ZM391 385C382 336 366 260 358 238C321 178 209 59 143 59C129 59 115 83 115 131C115 207 152 317 220 373C243 392 282 403 314 403C348 403 374 395 391 385Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,62.13,5.233)"><path d="M575 299C575 406 528 454 412 454C385 454 342 447 313 440L330 514L318 525C293 510 258 487 242 466L227 419C194 403 158 384 123 361L126 327C155 342 183 355 220 364L107 -148C96 -198 76 -210 19 -215L14 -253L259 -241V-206L240 -205C184 -202 183 -188 192 -141L220 -1C242 -10 269 -12 284 -12C352 5 434 48 484 102C542 165 575 238 575 299ZM479 290C479 170 380 41 305 41C281 41 249 60 237 72L300 395C329 399 353 401 374 401C426 401 479 377 479 290Z"></path></g><g transform="matrix(.013,0,0,-0.013,67.058,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></p>

Journal of Mathematics

Prismatic Sets Associated with Planar Rooted Trees

Figure 2