Observations on the parity of the total number of parts in odd--part partitions.
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.
Odd cutsets and the hard-core model on
We consider the hard-core lattice gas model on and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds , the model exhibits multiple hard-core measures, thus improving the previous bound of given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...
Odd graphs
Odd symplectic groups.
On a balanced property of derangements.
On a certain analogy of Stirling's numbers of the 2nd kind
On a certain numbering of the vertices of a hypergraph
On a class of combinatorial Diophantine equations.
On a class of combinatorial sums involving generalized factorials.
On a class of equations with special degrees over finite fields
On a class of polynomials associated with the cliques in a graph and its applications.
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