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math.CO2024
Alternative Proof of the Determinant of Complete Non-Ambiguous Trees
Daniel Chen
Complete non-ambiguous trees have been studied in various contexts. Recently, a conjecture was made about their determinants, and subsequently proved by Aval. An alternative proof…
math.CO2023
Expected Number of Dice Rolls Until an Increasing Run of Three
Daniel Chen
A closed form is found for the expected number of rolls of a fair n-sided die until three consecutive increasing values are seen. The answer is rational, and the greatest common di…
math.CO2022
Associated Permutations of Complete Non-Ambiguous Trees
Daniel Chen, Sebastian Ohlig
We explore new connections between complete non-ambiguous trees (CNATs) and permutations. We give a bijection between tree-like tableaux and a specific subset of CNATs. This map is…