The perfect balanced tree representing players and matches at a tennis Grand Slam. Australian Open, 2022. Women's singles
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"AUS Open is a tennis tournament attended by $𝑁=128=2^7$ women players. It is a balanced knokout tournament, \n",
"consisting in 7 rounds. Before the starting a draw is released for the first round.\n",
"Then succesivelly, the $(2𝑘-1)^{th}$ and $(2𝑘)^{th}$ winners in a round, $r\\geq 1$, $𝑘=1,...,2^{7-r}$ play together in the $(r+1)^{th}$ round. After the $6^{th}$ round the last two players have the final match, and the winner is the winner of the Grand Slam. The whole process is visualized by WTA as a balanced binary tree, having as root the tournament's winner, and the as tree nodes, the players in each round. The parent of a pair (2𝑘-1,2𝑘) playing in a round r is the winner of the corresponding match.\n",
"\n",
"We define as tree leafs the players from the second round, to avoid a cluttered tree visualization.\n",
"The node positions, assigned by Shell network layout, are rotated by an angle to get a symmetric circular tree. \n",
"The edges emanating from the a node pair (2k-1, 2k), representing players playing each other in the $r^{th}$, are drawn as a continuous/dotted line, depending on whether the match has been won/lost by that player.\n"
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"The matches results are recorded in a csv file of 127 rows. The players from the second round are recorded in the lines $2^6:2^7-1$, i.e. 64:127, and similarly\n",
"in the $r^{th}$, round, r=3, from $2^5:2^6-1$, and so on. In the $6^{th}$ round the finalists are recorded in the line 2 and 3,\n",
"and the winner in the first line.\n",
"\n",
"Information on the match result is recorded in the column \"won_lost\". 1, repsectively 2, is the code for a won/lost match.\n"
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