Eigenspace decompositions with respect to symmetrized incidence mappings.
Entropy of Schur–Weyl measures
Relative dimensions of isotypic components of th order tensor representations of the symmetric group on letters give a Plancherel-type measure on the space of Young diagrams with cells and at most rows. It was conjectured by G. Olshanski that dimensions of isotypic components of tensor representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to this family of Plancherel-type measures in the limit when converges to a constant. The main...
Envy-free cake divisions cannot be found by finite protocols.
Equivalence of a Number-Theoretical Problem with a Problem from the Graph Theory
Erdös-Ko-Rado from intersecting shadows
A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős-Ko-Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corresponding results.
Erdős-Ko-Rado theorems for uniform set-partition systems.
Erdős-Ko-Rado-type theorems for colored sets.
Evolutionary families of sets.
Extended Ramsey theory for words representing rationals
Ramsey theory for words over a finite alphabet was unified in the work of Carlson, who also presented a method to extend the theory to words over an infinite alphabet, but subject to a fixed dominating principle. In the present work we establish an extension of Carlson's approach to countable ordinals and Schreier-type families developing an extended Ramsey theory for dominated words over a doubly infinite alphabet (in fact for ω-ℤ*-located words), and we apply this theory, exploiting the Budak-Işik-Pym...
Extremal problems for -partite and -colorable hypergraphs.
Extremal subsets of avoiding solutions to linear equations in three variables.