2 problems

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The bivariate generating-function conjecture for first-step tree and map statistics
Fix $n\ge 2$ . Let $\\#T^F_1$ and $\\#M^F_1$ denote the first statistics for the tree and map associated with a random minimal transposition factorization, and let $\mathbb E$ denot…
Conjectureopengenerating-functions random-structures transpositionsarXiv posted 2 days ago
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The upper-bound conjecture for cyclically adjacent transpositions
Upper-bound conjecture. There always exists a cyclically adjacent swap such that
Conjectureopencombinatorics permutation-sorting transpositionsarXiv posted 2 days ago

The bivariate generating-function conjecture for first-step tree and map statistics