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

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Note on Packing Patterns in Colored Permutations

Packing patterns in permutations concerns finding the permutation with the maximum number of a prescribed pattern. In 2002, Albert, Atkinson, Handley, Holton and Stromquist showed that there always exists a layered permutation containing the maximum number of a layered pattern among all permutations of length n. Consequently the packing density for all but two (up to equivalence) patterns up to...

Optimal Packing Behavior of some 2-block Patterns

In this paper, a result of Albert, Atkinson, Handley, Holton, and Stromquist (Proposition 2.4 of [1]) which characterizes the optimal packing behavior of the pattern 1243 is generalized in two directions. The packing densities of layered patterns of type (1, α) and (1, 1, β) are computed. AMS Subject Classifications: 05A15, 05A16