Title: Weighted random staircase tableaux, asymmetric exclusion process, and generalized Eulerian polynomials. Abstract: Staircase tableaux are a relatively new combinatorial structure introduced by Sylvie Corteel and Lauren Williams in the context of the asymmetric exclusion process (ASEP) and Askey–Wilson polynomials. Since then, their purely combinatorial properties have gained considerable ...

The Robinson–Schensted–Knuth bijection, denoted by RSK, is a bijection between sequences π of real numbers of length n ≥ 1 and ordered pairs 〈P,Q〉 where P = P (π) is a semi–standard tableau with entries π1, . . . , πn, Q = Q(π) is a standard Young tableau with entries one through n, and P and Q both have shape λ = λ(π) where |λ| = n. Schensted’s theorem, which has been generalized by Greene, st...

The Robinson-Schensted correspondence, a bijection between nonnegative matrices and pair of tableaux, is investigated. The representation, in the tableau, of the dihedral symmetries of the matrix are derived in a simple manner using a shapepreserving anti-isomorphism of the platic monoid. The Robinson-Schensted correspondence is shown to be equivalent to the Hillman-Grass1 bijection between rev...

Shannon, A.G., J.C. Turner and K.T. Atanassov, A generalized tableau associated with colored convolution trees, Discrete Mathematics 92 (1991) 329-349. This paper considers the tableaux arising from the colors at different levels of arbitrary order convolution trees. The results are related to the elements which constitute the Pascal-LucasTurner triangles and to various generalizations of the F...

For example “i” is a YT of shape (4, 3, 1). The YT is said to be standard (an SYT) if the integers in the tableau are 1, 2,..., n as in “. A partition p = (pl, p2 ,..., pt) is strict if p1 > t+ > ... > pt > 0. A generalized Shzyted Young Tableau (abbreviated ST) of shape p is an array of n-integers into t rows with row i containing pi integers and indented i 1 spaces, such that the rows are non...

Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When integrators fractional steps Runge--Kutta methods, such can be written as generalized additive (GARK) thus representation analysis done through GARK framework. We show how general Butcher tableau linear stability related to coefficients splitting method, indi...