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22  Articles
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We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain spherical varietie... see more

Parking functions were classically defined for nn cars attempting to park on a one-way street with nn parking spots, where cars only drive forward. Subsequently, parking functions have been generalized in various ways, including allowing cars the option o... see more

In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect matchings.

We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain spherical varietie... see more

We determine the Solutions f : S ? H of the generalized Jensen’s functional equationf( x + s(y)) + f( x + t(y)) = 2f(x), x , y? Sand the solutions f : S ? H of the generalized quadratic functional equationf ( x + s(y)) + f (x + t(y)) = 2f (x) + 2f (y), &n... see more

In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect matchings.

A new descent set statistic on involutions, defined geometrically via their interpretation as matchings, is introduced in this paper, and shown to be equidistributed with the standard one. This concept is then applied to construct explicit cyclic descent ... see more

Several authors have recently considered the smallest positive part missing from an integer partition, known as the minimum excludant or mex.  In this work, we revisit and extend connections between Dyson's crank statistic, the mex, and Frobenius sym... see more

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern counts, both in ter... see more

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