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Integer partitions, tilings of 2 D -gons and lattices

Matthieu Latapy (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2 D -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2 D -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.

Integer Partitions, Tilings of 2D-gons and Lattices

Matthieu Latapy (2010)

RAIRO - Theoretical Informatics and Applications

In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.

Integral Cayley Sum Graphs and Groups

Xuanlong Ma, Kaishun Wang (2016)

Discussiones Mathematicae Graph Theory

For any positive integer k, let Ak denote the set of finite abelian groups G such that for any subgroup H of G all Cayley sum graphs CayS(H, S) are integral if |S| = k. A finite abelian group G is called Cayley sum integral if for any subgroup H of G all Cayley sum graphs on H are integral. In this paper, the classes A2 and A3 are classified. As an application, we determine all finite Cayley sum integral groups.

Integral representation of the n -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel

Emmanuel Fricain, Javad Mashreghi (2008)

Annales de l’institut Fourier

In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces ℋ ( b ) , where b is in the unit ball of H ∞ ( ℂ + ) . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces K b , where b is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel k ω , n b of evaluation...

Integrals of logarithmic and hypergeometric functions

Anthony Sofo (2016)

Communications in Mathematics

Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. In this paper we explore many relations and explicitly derive closed form representations of integrals of logarithmic, hypergeometric functions and the Lerch phi transcendent in terms of zeta functions and sums of alternating harmonic numbers.

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