On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs.
On a class of polynomials with integer coefficients.
On a combinatorial problem of Asmus Schmidt.
On a congruence for the number of finite marked topologies
On a conjecture of Andrews.
On a conjecture of Frankl and Füredi.
On a conjecture of Sárközy and Szemerédi
Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. In 1994, Sárközy and Szemerédi conjectured that there exist infinite additive complements A and B with lim sup A(x)B(x)/x ≤ 1 and A(x)B(x)-x = O(minA(x),B(x)), where A(x) and B(x) are the counting functions of A and B, respectively. We prove that, for infinite additive complements A and B, if lim sup A(x)B(x)/x ≤ 1, then, for any given M > 1,...
On a conjecture of Turán
On a family of generalized Pascal triangles defined by exponential Riordan arrays.
On a functional-difference equation of Runyon, Morrison, Carlitz, and Riordan.
On a generalization of binomial coefficients. (Sur une généralisation des coefficients binomiaux.)
On a generalization of duality triads
Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.
On a generalization of the Narayana triangle.
On a generalized recurrence for Bell numbers.
On a multiplicative partition function.
On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem
Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube...
On a new family of generalized Stirling and Bell numbers.
On a number pyramid related to the binomial, Deleham, Eulerian, MacMahon and Stirling number triangles.
On a partition function of Richard Stanly.
On a Problem of D'Atri and Nickerson.