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math.CO2026
Ordered set partition posets
Bruce E Sagan, Sheila Sundaram
A set partition is said to be ordered if the blocks of the partition are listed in a specific order. The ordered set partitions of , with a unique minimal element a…
math.CO2026
K-promotion on m-packed labelings of posets
Jamie Kimble, Bruce E. Sagan, Avery St. Dizier
Schutzenberger's promotion operator, pro, is a fundamental map in dynamical algebraic combinatorics. At first, its action was mainly considered on standard Young tableaux. But pro…
math.CO2025
Hyperbinary partitions and q-deformed rationals
Thomas McConville, James Propp, Bruce E. Sagan
A hyperbinary partition of the nonnegative integer n is a partition where every part is a power of 2 and every part appears at most twice. We give three applications of the length…