Powers of the Vandermonde determinant, Schur Functions, and recursive formulas

Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, we give recursive formulas for the coefficient of the Schur function s_{\m} in the decomposition of an even power of the Vandermonde determinant in $n + 1$ variables in terms of the coefficient of the Schur function s_{\l} in the decomposition of the same even power of the Vandermonde determinant in $n$ variables if the Young diagram of \m is obtained from the Young diagram of \l by adding a tetris type shape to the top or to the left. An extended abstract containing the statement of the results presented here appeared in the Proceedings of FPSAC11Comment: 23 pages; extended abstract appeared in the Proceedings of FPSAC1

A method and technique for installing light-weight fragile, high-temperature fiber insulation

A method of installing fragile, light-weight, high-temperature fiber insulation, particularly where the insulation is to be used as a seal strip providing a high order of thermal barrier insulation is described. The process is based on provision of a strip of the mineral batting cut oversize by a predetermined amount, saturated in a fugitive polymer solution, compressed in a mold, dried and cured to form a rigidized batting material which may be machined to required shape. The machined dimensions would normally be at least nominally less than the dimensions of the cavity to be sealed. After insertion in the cavity, which may be a wire-mesh seal enclosure, the apparatus is subjected to baking at a temperature sufficiently high to cause the resin to burn off cleanly, leaving the batting substantially in its original condition and expanded into the cavity or seal enclosure