We prove that the permutations of $\{1,\dots, n\}$ having an increasing (resp., decreasing) subsequence length $n-r$ index a subset set all $r$th Kronecker powers $n \times n$ permutation matrices which is basis for linear span set. Thanks to known Schur-Weyl duality, this gives new centralizer algebra partition acting on tensor power vector space. give some related results doubly stochastic in...

We consider the Hamiltonian cycle problem (HCP) embedded in a controlled Markov decision process. In this setting, HCP reduces to an optimization problem on a set of Markov chains corresponding to a given graph. We prove that Hamiltonian cycles are minimizers for the trace of the fundamental matrix on a set of all stochastic transition matrices. In case of doubly stochastic matrices with symmet...