Lower bounds for packing densities

1991 ◽  
Vol 57 (3-4) ◽  
pp. 291-311 ◽  
Author(s):  
K. Bezdek ◽  
R. Connelly
Keyword(s):  
Lower Bounds ◽  
Packing Densities

scholarly journals On Packing Densities of Permutations

10.37236/1622 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
M. H. Albert ◽  
M. D. Atkinson ◽  
C. C. Handley ◽  
D. A. Holton ◽  
W. Stromquist
Keyword(s):  
Lower Bounds ◽  
Maximum Density ◽  
Upper And Lower Bounds ◽  
Maximal Density ◽  
Permutation Pattern ◽  
Packing Densities

The density of a permutation pattern $\pi$ in a permutation $\sigma$ is the proportion of subsequences of $\sigma$ of length $|\pi|$ that are isomorphic to $\pi$. The maximal value of the density is found for several patterns $\pi$, and asymptotic upper and lower bounds for the maximal density are found in several other cases. The results are generalised to sets of patterns and the maximum density is found for all sets of length $3$ patterns.

scholarly journals Determining Lower Bounds for Packing Densities of Non-layered Patterns Using Weighted Templates

10.37236/774 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Cathleen Battiste Presutti
Keyword(s):  
Lower Bounds ◽  
Packing Density ◽  
Permutation Pattern ◽  
Maximum Proportion ◽  
Limiting Value ◽  
Packing Densities

The packing density of a permutation pattern $\pi$ is the limiting value, ${n}$ $\rightarrow$ $\infty$, of the maximum proportion of subsequences of $\sigma$ $\in$ ${S_{n}}$ that are order-isomorphic to $\pi$. We generalize methods for obtaining lower bounds for the packing density of any pattern and demonstrate the methods' usefulness when patterns are non-layered.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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