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math.CO2026
A Combinatorial Proof of Cayley's Formula via Degree Sequences
Helia Karisani, Mohammadreza Daneshvaramoli
Cayley's formula is a fundamental result in combinatorics that counts the number of labeled trees on n vertices. While existing proofs use approaches such as Prufer sequences and t…
cs.DS2026
The Secretary Problem with Predictions and a Chosen Order
Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi +2
We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023), in which the decision-maker has access to machine-learned predictio…