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- Mark Dukes, Robert Parviainen
- Electr. J. Comb.
- 2010

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)

- Richard Brak, Sylvie Corteel, John W. Essam, Robert Parviainen, Andrew Rechnitzer
- Electr. J. Comb.
- 2006

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)

- Robert Parviainen
- Combinatorics, Probability & Computing
- 2004

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 count the number of permutations with k occurrences of the pattern 2–13 in permutations by lattice path enumeration. We give closed forms for k ≤ 8, extending results of Claesson and Mansour.

- Sven Erick Alm, Robert Parviainen
- Combinatorics, Probability & Computing
- 2002

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 give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff.

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)

For each pair of graphs from among the Archimedean lattices and their dual Laves lattices we demonstrate that one is a subgraph of the other or prove that neither can be a subgraph of the other. Therefore, we determine the entire partial ordering by inclusion of these 19 infinite periodic graphs. There are a total of 72 inclusion relationships, of which 35… (More)

We give examples of pairs of planar, quasi-transitive graphs with connective constants and critical probabilities in the same order.