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math.CO2022
On the cancellation-free antipode formula for the Malvenuto-Reutenauer Hopf Algebra
Da Xu, Houyi Yu
For the Malvenuto-Reutenauer Hopf algebra of permutations, we provide a cancellation-free antipode formula for any permutation of the form $ab1\cdots(b-1)(b+1)\cdots(a-1)(a+1)\cdot…
math.CO2022
The weak order on the hyperoctahedral group and the monomial basis for the Hopf algebra of signed permutations
Houyi Yu
We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted pro…