Polynomial identities which imply identities of Euler and Jacobi
Polynomial sequences generated by infinite Hessenberg matrices
We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz...
Polynomials of multipartitional type and inverse relations
Chou, Hsu and Shiue gave some applications of Faà di Bruno's formula to characterize inverse relations. Our aim is to develop some inverse relations connected to the multipartitional type polynomials involving to binomial type sequences.
Poset homology of Rees products, and -Eulerian polynomials.
Positions of value in generalized domineering and chess.
Positivity of three-term recurrence sequences.
Potenzen der Pascalmatrix und eine Identität der Kombinatorik.
Powers of a matrix and combinatorial identities.
Prefix exchanging and pattern avoidance by involutions.
Primal-dual approximation algorithms for a packing-covering pair of problems
We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and...
Primal-dual approximation algorithms for a packing-covering pair of problems
We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and...
Prime divisors of -binomial coefficients
Prime factors of binomial coefficients and related problems
Primitive words and spectral spaces.
Probabilistic proofs of hook length formulas involving trees.
Probabilities as values of modular forms and continued fractions.
Probability measures corresponding to Aval numbers
We describe the class of probability measures whose moments are given in terms of the Aval numbers. They are expressed as the multiplicative free convolution of measures corresponding to the ballot numbers .
Probability that an element of a finite group has a square root
Let G be a finite group of even order. We give some bounds for the probability p(G) that a randomly chosen element in G has a square root. In particular, we prove that p(G) ≤ 1 - ⌊√|G|⌋/|G|. Moreover, we show that if the Sylow 2-subgroup of G is not a proper normal elementary abelian subgroup of G, then p(G) ≤ 1 - 1/√|G|. Both of these bounds are best possible upper bounds for p(G), depending only on the order of G.
Problemas combinatorios sobre bases aditivas.
Problemas da teoria dos grafos e a sua relação com os problemas da cobertura e da partição de um conjunto