Packing densities of layered permutations and the minimum number of monotone sequences in layered permutations

Author(s)

Bastos, Josefran de Oliveira ^[1] ; Coregliano, Leonardo Nagami ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

• Document type: Journal article
• Source: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE; v. 18, n. 2 2016.
• Web of Science Citations: 0

Abstract

In this paper, we present two new results of layered permutation densities. The first one generalizes theorems from Hasto (2003) and Warren (2004) to compute the permutation packing of permutations whose layer sequence is (1(a), l(1), l(2), ... , l(k)) with 2(a)-a-1 >= k (and similar permutations). As a second result, we prove that the minimum density of monotone sequences of length k + 1 in an arbitrarily large layered permutation is asymptotically 1/k(k). 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). (AU)

• FAPESP's process: 13/23720-9 - The Asymptotic Combinatorics of Permutations and Flag Algebras
• Grantee: Leonardo Nagami Coregliano
• Support Opportunities: Scholarships in Brazil - Master