O Josephově problému
Objects counted by the central Delannoy numbers.
Objets simpliciaux
Od unimodálních posloupností k narozeninovému paradoxu
Konečná posloupnost reálných čísel se nazývá unimodální, pokud ji lze rozdělit na neklesající a nerostoucí úsek. V textu se zaměříme především na kombinatorické posloupnosti tvořené kombinačními čísly nebo Stirlingovými čísly prvního a druhého druhu. Kromě unimodality se budeme věnovat též příbuznému pojmu logaritmické konkávnosti. Ukážeme, jak tato témata souvisejí s klasickými Newtonovými a Maclaurinovými nerovnostmi, které v závěru využijeme k řešení obecné verze narozeninového paradoxu.
On a certain analogy of Stirling's numbers of the 2nd kind
On a class of combinatorial Diophantine equations.
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 congruence for the number of finite marked topologies
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 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.
On a problem of Steinhaus concerning binary sequences.