Independent sets on path-schemes.
Inequalities for a Pair of Maps S x S ... S with S a Finite Set.
Inequalities for chains of normalized symmetric sums.
Inequalities Involving Maps of Finite Sets.
Inequalities of Bonferroni-Galambos type with applications to the Tutte polynomial and the chromatic polynomial.
Infinite families of divisibility properties modulo 4 for non-squashing partitions into distinct parts.
Infinite products over hyperpyramid lattices.
Infinite products over visible lattice points.
Integer partitions and convexity.
Integer partitions, tilings of -gons and lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -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 -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
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.
Integer partitions with fixed subsums.
Integer sequences and matrices over finite fields.
Integer sequences related to compositions without 2's.
Integral representation of the -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel
In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces , where is in the unit ball of . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces , where 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 of evaluation...
Integral representations and binomial coefficients.
Integral representations of Catalan and related numbers.
Integrals and polygamma representations for binomial sums.
Integrals of logarithmic and hypergeometric functions
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.
Integration over a Simplex, Truncated Cubes, and Eulerian Numbers.