1,3

Let X be a p X q rectangular matrix with random Gaussian entries. Expand E( tr (X'*X)^n ) as a polynomial in p and q for fixed n. Sequence gives coefficient of least significant term in polynomial.

There should be a reference to a paper by Guy et al. (?) that gives a formula.

An n-swap move consists of the removal of n edges and addition of n different edges which result in a new tour. A sequential n-swap is one in which the union of the n removed and n added edges forms a single cycle. The type can be characterized by how the n segments of the original tour formed by the removal are reassembled.

P. J. Hanlon, R. P. Stanley and J. R. Stembridge, Some combinatorial aspects of the spectra of normally distributed random matrices. Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991), 151-174, Contemp. Math., 138, Amer. Math. Soc., Providence, RI, 1992.

David L. Applegate, Robert E. Bixby, Vasek Chvatal and William J. Cook, The Traveling Salesman Problem: A Computational Study, Princeton UP, 2006, Table 17.1, p. 535 (has 1358 instead of 1348 for n = 6)

Keld Helsgaun, An Effective Implementation of K-opt Movesfor the Lin-Kernighan TSP Heuristic.

Hanlon et al. give a formula (it would be nice to give it here).

A complicated formula from Hanlon is given on page 23 of Helsgaun. - Rob Pratt (Rob.Pratt(AT)sas.com), Mar 30 2007

Cf. A061714.

Sequence in context: A034216 A117887 A082988 this_sequence A094070 A119022 A006682

Adjacent sequences: A001168 A001169 A001170 this_sequence A001172 A001173 A001174

nonn,nice

C. L. Mallows (colinm(AT)research.avayalabs.com)

Additional comments from David Applegate (david(AT)research.att.com), Jun 21 2001