7 citations · 9 across the 4 of their papers we have counts for
5 papers
On the Möbius function of permutations under the pattern containment order
David Marchant
We study several aspects of the Möbius function, , on the poset of permutations under the pattern containment order. First, we consider cases where the lower bound of the p…
2413-balloon permutations and the growth of the Möbius function
David Marchant
We show that the growth of the principal Möbius function on the permutation poset is exponential. This improves on previous work, which has shown that the growth is at least polyno…
Zeros of the Möbius function of permutations
Robert Brignall, Vít Jelínek, Jan Kynčl +1
We show that if a permutation contains two intervals of length 2, where one interval is an ascent and the other a descent, then the Möbius function of the interval $[1,π…
Intervals of permutations and the principal Möbius function
Robert Brignall, David Marchant
We show that the proportion of permutations of length with principal Möbius function equal to zero, , is asymptotically bounded below by 0.3995. If a permutation cont…
The Möbius function of permutations with an indecomposable lower bound
Robert Brignall, David Marchant
We show that the Möbius function of an interval in a permutation poset where the lower bound is sum (resp. skew) indecomposable depends solely on the sum (resp. skew) indecomposabl…