Higher order matching polynomials and $d$-orthogonality TeX Export

@article{citeulike:5773372, abstract = {We show combinatorially that the higher-order matching polynomials of severalfamilies of graphs are d-orthogonal polynomials. The matching polynomial of agraph is a generating function for coverings of a graph by disjoint edges; thehigher-order matching polynomial corresponds to coverings by paths. Severalfamilies of classical orthogonal polynomials -- the Chebyshev, Hermite, andLaguerre polynomials -- can be interpreted as matching polynomials of paths,cycles, complete graphs, and complete bipartite graphs. The notion ofd-orthogonality is a generalization of the usual idea of orthogonality forpolynomials and we use sign-reversing involutions to show that the higher-orderChebyshev (first and second kinds), Hermite, and Laguerre polynomials ared-orthogonal. We also investigate the moments and find generating functions ofthose polynomials.}, archivePrefix = {arXiv}, author = {Drake, Dan}, citeulike-article-id = {5773372}, citeulike-linkout-0 = {http://arxiv.org/abs/0909.1655}, citeulike-linkout-1 = {http://arxiv.org/pdf/0909.1655}, day = {9}, eprint = {0909.1655}, keywords = {chebyshev, combinatorics, d-orthogonality, hermite, laguerre, op}, month = {Sep}, posted-at = {2009-09-11 09:48:17}, priority = {0}, title = {Higher order matching polynomials and \$d\$-orthogonality}, url = {http://arxiv.org/abs/0909.1655}, year = {2009} }

TY - JOUR ID - citeulike:5773372 L3 - citeulike-article-id:5773372 N2 - We show combinatorially that the higher-order matching polynomials of severalfamilies of graphs are d-orthogonal polynomials. The matching polynomial of agraph is a generating function for coverings of a graph by disjoint edges; thehigher-order matching polynomial corresponds to coverings by paths. Severalfamilies of classical orthogonal polynomials -- the Chebyshev, Hermite, andLaguerre polynomials -- can be interpreted as matching polynomials of paths,cycles, complete graphs, and complete bipartite graphs. The notion ofd-orthogonality is a generalization of the usual idea of orthogonality forpolynomials and we use sign-reversing involutions to show that the higher-orderChebyshev (first and second kinds), Hermite, and Laguerre polynomials ared-orthogonal. We also investigate the moments and find generating functions ofthose polynomials. TI - Higher order matching polynomials and $d$-orthogonality KW - chebyshev KW - combinatorics KW - d-orthogonality KW - hermite KW - laguerre KW - op AU - Drake, Dan PY - 2009/Sep/09/ UR - http://arxiv.org/abs/0909.1655 ER -