The reverse mathematics of non-decreasing subsequences

Enumerating rc-Invariant Permutations with No Long Decreasing Subsequences∗

We use the Robinson-Schensted-Knuth correspondence and Schützenberger’s evacuation of standard tableaux to enumerate permutations and involutions which are invariant under the reverse-complement map and which have no decreasing subsequences of length k. These enumerations are in terms of numbers of permutations with no decreasing subsequences of length approximately k2 ; we use known results co...

Increasing and Decreasing Subsequences and Their Variants

We survey the theory of increasing and decreasing subsequences of permutations. Enumeration problems in this area are closely related to the RSK algorithm. The asymptotic behavior of the expected value of the length is(w) of the longest increasing subsequence of a permutation w of 1, 2, . . . , n was obtained by Vershik-Kerov and (almost) by Logan-Shepp. The entire limiting distribution of is(w...

Increasing Subsequences in Nonuniform Random Permutations

Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear group to obtain results about the longest increasing and decreasing subsequences in non-uniform random permutations.

MHD Jeffrey NanoFluids Flow Over a Stretching Sheet Through a Porous Medium in Presence of Nonlinear Thermal Radiation and Heat Generation/Absorption

In this article, a numerical investigation of magnetohydrodynamic non-Newtonian nanofluid flow on a stretching sheet through an isotropic porous medium. The effects of both non-linear thermal radiation and heat generation/absorption were studied on distributions of velocity, temperature and concentration. On the other side, the governing partial differential equations have been transformed by u...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS