منابع مشابه
Enumerative Properties of Ferrers Graphs
We define a class of bipartite graphs that correspond naturally with Ferrers diagrams. We give expressions for the number of spanning trees, the number of Hamiltonian paths when applicable, the chromatic polynomial and the chromatic symmetric function. We show that the linear coefficient of the chromatic polynomial is given by the excedance set statistic.
متن کاملBoolean complexes for Ferrers graphs
In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show that the boolean numbers of the associated Ferrers graphs are the Genocchi numbers of the second kind, and obtain a relation between the Legen...
متن کاملFerrers Graphs and Related Ideals
This abstract is essentially taken from the introduction of the paper Monomial and toric ideals associated to Ferrers graphs [13], written jointly with Alberto Corso. A Ferrers graph is a bipartite graph on two distinct vertex sets X = {x1, . . . , xn} and Y = {y1, . . . , ym} such that if (xi, yj) is an edge of G, then so is (xp, yq) for 1 ≤ p ≤ i and 1 ≤ q ≤ j. In addition, (x1, ym) and (xn, ...
متن کاملEnumerative properties of generalized associahedra
Some enumerative aspects of the fans called generalized associahedra, introduced by S. Fomin and A. Zelevinsky in their theory of cluster algebras, are considered in relation with a bicomplex and its two spectral sequences. A precise enumerative relation with the lattices of generalized noncrossing partitions is conjectured and some evidence is given.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1135-1