Advances in Applied Mathematics

A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al., where 25 out of 65 non-equivalent cases were solved. In this paper, we give 27 distribution results for these patterns including 14 ...

Let Δ be a connected, pure 2-dimensional simplicial complex embedded in R 2 and let C r ( Δ ˆ ) be the homogenized spline module of Δ with smoothness r as in [7]. To study C r ( Δ ˆ ), Schenck and Stillman developed in [7] the quotient ...

In this paper we investigate the complexity of model selection and model testing for dynamical systems with toric steady states. Such systems frequently arise in the study of chemical reaction networks. We do this by formulating these ...

We prove the cancellation-free formula for the antipode of the noncrossing partition lattice in the reduced incidence Hopf algebra of posets due to Einziger. The proof is based on a map from chains in the noncrossing partition lattice ...

A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein series involved in Ramanujan's formula for ζ ( 2 m + 1 ). ...

The distribution of certain Mahonian statistic (called BAST) introduced by Babson and Steingrímsson over the set of permutations that avoid vincular pattern 1 32 _, is shown bijectively to match the distribution of major index over the ...

Let the polynomial b n ( t ) be defined as the n-th coefficient in the power series expansion (in variable x) of the function B ( t , x ) = ∏ n = 0 ∞ 1 1 − t x 2 n = ∑ n = 0 ∞ b n ( t ) x n . ...

The Turán inequality and its higher order analog arise in the study of Maclaurin coefficients of an entire function in the Laguerre-Pólya class. It is well known that if a real entire function ψ ( x ) is in the LP class, the Maclaurin ...

The group of basis-conjugating automorphisms of the free group of rank n, also known as the McCool group or the welded braid group P Σ n, contains a much-studied subgroup, called the upper McCool group P Σ n +. Starting from the ...

A general family of matrix valued Hermite type orthogonal polynomials is introduced as the matrix orthogonal polynomials with respect to a weight. The matrix polynomials are eigenfunctions of a matrix differential equation. For the ...

Given a ruled surface V defined in the standard parametric form P ( t 1 , t 2 ), we present an algorithm that determines the singularities (and their multiplicities) of V from the parametrization P. More precisely, from P we construct ...

We consider two extensions of free probability that have been studied in the research literature, and are based on the notions of c-freeness and respectively of infinitesimal freeness for noncommutative random variables. In a 2012 ...

We study the relation between the cluster automorphisms and the quasi-automorphisms of a cluster algebra A. We prove that under some mild condition, satisfied for example by every skew-symmetric cluster algebra, the quasi-automorphism ...

This paper introduces Dirichlet arrangements, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize combinatorial results on graphic arrangements to ...

In the paper ‘A probabilistic analysis of a discrete-time evolution in recombination’ [4] the evolution of the recombination transformation Ξ = ∑ δ ρ δ ⨂ J ∈ δ μ J was described by a Markov chain ( Y n ) on a set of partitions, which ...