3 research outputs found
Packing densities of layered permutations and the minimum number of monotone sequences in layered permutations
In this paper, we present two new results of layered permutation densities.
The first one generalizes theorems from H\"{a}st\"{o} (2003) and Warren (2004)
to compute the permutation packing of permutations whose layer sequence
is~ with~ (and similar
permutations). As a second result, we prove that the minimum density of
monotone sequences of length~ in an arbitrarily large layered permutation
is asymptotically~. This value is compatible with a conjecture from
Myers (2003) for the problem without the layered restriction (the same problem
where the monotone sequences have different lengths is also studied).Comment: 24 page
Packing densities of layered permutations and the minimum number of monotone sequences in layered permutations
In this paper, we present two new results of layered permutation densities.
The first one generalizes theorems from H\"{a}st\"{o} (2003) and Warren (2004)
to compute the permutation packing of permutations whose layer sequence
is~ with~ (and similar
permutations). As a second result, we prove that the minimum density of
monotone sequences of length~ in an arbitrarily large layered permutation
is asymptotically~. This value is compatible with a conjecture from
Myers (2003) for the problem without the layered restriction (the same problem
where the monotone sequences have different lengths is also studied)
Packing densities of layered permutations and the minimum number of monotone sequences in layered permutations
In this paper, we present two new results of layered permutation densities.The first one generalizes theorems from H\"{a}st\"{o} (2003) and Warren (2004)to compute the permutation packing of permutations whose layer sequenceis~ with~ (and similarpermutations). As a second result, we prove that the minimum density ofmonotone sequences of length~ in an arbitrarily large layered permutationis asymptotically~. This value is compatible with a conjecture fromMyers (2003) for the problem without the layered restriction (the same problemwhere the monotone sequences have different lengths is also studied).Comment: 24 page