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Let S âŠ‚ {âˆ’1, 0, 1}2 \ {(0, 0)}. We address the enumeration of plane lattice walks with steps in S, that start from (0, 0) and always remain in the first quadrant {(i, j) : i â‰¥ 0, j â‰¥ 0}. A priori,â€¦ (More)

- Marni Mishna, Andrew Rechnitzer
- Theor. Comput. Sci.
- 2009

We present two classes of random walks restricted to the quarter plane whose generating function is not holonomic. The non-holonomy is established using the iterated kernel method, a recent variantâ€¦ (More)

We introduce k-crossings and k-nestings of permutations. We show that the crossing number and the nesting number of permutations have a symmetric joint distribution. As a corollary, the number ofâ€¦ (More)

- Stephen Melczer, Marni Mishna
- Combinatorics, Probability & Computing
- 2014

We provide exact and asymptotic counting formulas for five singular lattice path models in the quarter plane. Furthermore, we prove that these models have a non D-finite generating function. RÃ©sumÃ©â€¦ (More)

- Marni Mishna
- J. Comb. Theory, Ser. A
- 2009

This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walksâ€¦ (More)

- FrÃ©dÃ©ric Chyzak, Marni Mishna, Bruno Salvy
- J. Comb. Theory, Ser. A
- 2005

Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a largeâ€¦ (More)

For positive integers s and t, let f (sÃ’ t) denote the smallest positive integer N such that every 2-colouring of [1Ã’N] = f1Ã’ 2Ã’ ï£¿ ï£¿ ï£¿ Ã’Ng has a monochromatic homothetic copy of f1Ã’ 1 + sÃ’ 1 + s +â€¦ (More)

- Marni Mishna
- 2006

Using an algorithm for computing the symmetric function Kronecker product of D-finite symmetric functions we find some new Kronecker product identities. The identities give closed form formulas forâ€¦ (More)

- EXIGENCE PARTIELLE, JULIE MISHNA NOVEMBRE, Marni Mishna, Vicki Munn
- 2003

The theory of holonomic systems has proven a valuable tool for automatic proofs of combinatorial identities. The scalar product of symmetric functions provides a useful way to phrase many problems inâ€¦ (More)

- Sophie Burrill, Julien Courtiel, Ã‰ric Fusy, Stephen Melczer, Marni Mishna
- Eur. J. Comb.
- 2016

Walks on Youngâ€™s lattice of integer partitions encode many objects of algebraic and combinatorial interest. Chen et al. established connections between such walks and arc diagrams. We show that walksâ€¦ (More)