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In the two main results presented here we give representations as products ofbidiagonal matrices for the production matrices of certain generatingpolynomials of lattice paths and we show that those production matrices are theHessenberg matrices associated with the components of the decomposition ofsymmetric multiple orthogonal polynomials. As a consequence of these results,we can use the recently found connection between lattice paths, branchedcontinued fractions, and multiple orthogonal polynomials to analyse symmetricmultiple orthogonal polynomials.  We revisit known results about the location of the zeros of symmetricmultiple orthogonal polynomials, we find combinatorial interpretations for themoments of the dual sequence of a symmetric multiple orthogonal polynomialsequence, we give an explicit proof of the existence of orthogonality measuressupported on a starlike set for symmetric multiple orthogonal polynomials withpositive recurrence coefficients as well as orthogonality measures on thepositive real line for the components of the decomposition of these symmetricmultiple orthogonal polynomials, and we give explicit formulas as terminatinghypergeometric series for Appell sequences of symmetric multiple orthogonalpolynomials with respect to an arbitrary number of measures whose densities canbe expressed via Meijer G-functions.

Bidiagonal matrix factorisations associated with symmetric multiple orthogonal polynomials and lattice paths