Robert Parviainen

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This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics on these structures under this bijection and prove that some of these statistics are equidistributed. Several special(More)
We give a combinatorial derivation and interpretation of the algebra associated with the stationary distribution of the partially asymmetric exclusion process. Our derivation works by constructing a larger Markov chain on a larger set of generalised configurations. A bijection on this new set of configurations allows us to find the stationary distribution(More)
The random assignment problem is to minimize the cost of an assignment in a n×n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2, . . . , m, for m = n or n, and random permutations of 1, 2, . . . , n for each row, or of 1, 2, . . . , n for the whole matrix.(More)
We present improved lower and upper bounds for the time constant of first-passage percolation on the square lattice. For the case of lower bounds, a new method, using the idea of a transition matrix, has been used. Numerical results for the exponential and uniform distributions are presented. A simulation study is included, which results in new estimates(More)
We find the generating function of self-avoiding walks and trails on a semi-regular lattice called the 3.122 lattice in terms of the generating functions of simple graphs, such as self-avoiding walks, polygons and tadpole graphs on the hexagonal lattice. Since the growth constant for these graphs is known on the hexagonal lattice we can find the growth(More)
We introduce weighted succession rules and parametric production matrices — simple extensions of the standard ECO method succession rules and production matrices. The purpose is to enumerate combinatorial objects with respect to several variables. We consider one main example, from the theory of Dyck paths. The path statistics primarily considered are peak(More)