127 citations · 452 across the 42 of their papers we have counts for
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Proof of a conjecture by Starr and log-concavity for random commuting permutations
Abdelmalek Abdesselam
We prove a conjecture by Shannon Starr regarding the asymptotics for the number of tuples of commuting permutations with given number of joint orbits. These numbers generalize unsi…
Bessenrodt--Ono inequalities for -tuples of pairwise commuting permutations
Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser
Let denote the symmetric group. We consider \begin{equation*} N_{\ell}(n) := \frac{\left\vert Hom\left( \mathbb{Z}^{\ell},S_n\right) \right\vert}{n!} \end{equation*} which al…
On a mod property of -tuples of pairwise commuting permutations
Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser
Let denote the symmetric group of permutations acting on elements. We investigate the double sequence counting the number of tuples of elements o…
A bijection for tuples of commuting permutations and a log-concavity conjecture
Abdelmalek Abdesselam, Pedro Brunialti, Tristan Doan +1
Let denote the number of -tuples of commuting permutations of elements whose permutation action results in exactly orbits or connected components. We pr…
Log-concavity with respect to the number of orbits for infinite tuples of commuting permutations
Abdelmalek Abdesselam
Let be the number of -tuples of commuting permutations of elements whose permutation action results in exactly orbits or connected components. We formulate th…
A local injective proof of log-concavity for increasing spanning forests
Abdelmalek Abdesselam
We give an explicit combinatorial proof of a weighted version of strong log-concavity for the generating polynomial of increasing spanning forests of a finite simple graph equipped…