Determinantal generating functions of colored spanning forests.
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.
There exists a bijection between one-stack sortable permutations (permutations which avoid the pattern (231)) and rooted plane trees. We define an edit distance between permutations which is consistent with the standard edit distance between trees. This one-to-one correspondence yields a polynomial algorithm for the subpermutation problem for (231) pattern-avoiding permutations. Moreover, we obtain the generating function of the edit distance between ordered unlabeled trees and some special ones. For...