Markus Fulmek

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Abstract. We generalize the classical work of de Bruijn, Knuth and Rice (giving the asymptotics of the average height of Dyck paths of length n) to the case of p– watermelons with a wall (i.e., to a certain family of p nonintersecting Dyck paths; simple Dyck paths being the special case p = 1.) We work out this asymptotics for the case p = 2 only, since the(More)
We consider the problem of enumerating the permutations containing exactly k occurrences of a pattern of length 3. This enumeration has received a lot of interest recently, and there are a lot of known results. This paper presents an alternative approach to the problem, which yields a proof for a formula which so far only was conjectured (by Noonan and(More)
Let a, b and c be positive integers, and consider a hexagon with side lengths a, b, c, a, b, c whose angles are 120◦ (see Figure 1.a). The subject of enumerating rhombus tilings of this hexagon (cf. Figure 1.b; here, and in the sequel, by a rhombus we always mean a rhombus with side lengths 1 and angles of 60◦ and 120◦) gained a lot of interest recently.(More)
In [4], Gurevich, Pyatov and Saponov stated an expansion for the product of two Schur functions and gave a proof based on the Plücker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which was stated and proved in [1, Lemma 16]. In [1], it was used to prove bijectively Dodgson’s condensation(More)
We give bijective proofs for Jacobi{Trudi-type and Giambelli-type identities for symplectic and orthogonal characters. These proofs base on interpreting King and El-Sharkaway's symplectic tableaux, Proctor's odd and intermediate symplectic tableaux, Proctor's and King and Welsh's orthogonal tableaux, and Sundaram's odd orthogonal tableaux in terms of(More)
The purpose of this note is to exhibit clearly how the “graphical condensation” identities of Kuo, Yan, Yeh and Zhang follow from classical Pfaffian identities by the Kasteleyn–Percus method for the enumeration of matchings. Knuth termed the relevant identities “overlapping Pfaffian” identities and the key concept of proof “superpositions of matchings”. In(More)
In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindström–Gessel–Viennotmethod and the Jacobi-Trudi identity together with elementary observations. After some preparations, this point of view provides “graphical proofs” for classical determinantal identities like the(More)