Lim Ulrich sequences and Lech’s conjecture

Fraenkel's conjecture for six sequences

Almost Regular Sequences and the Monomial Conjecture

This conjecture has assumed a central role since it has a very simple statement and it implies several other important conjectures, notably the Canonical Element Conjecture, for rings of positive or mixed characteristic. In fact, when this conjecture was first announced, it had numerous further consequences, some of which, such as the New Intersection Conjecture, were proved later by different ...

Contentious Contracts ¤ Ulrich Hege

This paper o¤ers an explanation of rationally incomplete contracts where incompleteness refers to unforeseen contingencies. Agents enter a relationship with two-sided moral hazard in which a commitment to discard parts of the joint resources may be ex ante e¢cient. This happens through costly legal dispute which arises when contract terms are missing for the undesirable outcomes. We show that a...

On Bialostocki’s Conjecture for Zero-sum Sequences

A finite sequence S of terms from an (additive) abelian group is said to have zero-sum if the sum of the terms of S is zero. In 1961 P. Erdős, A. Ginzburg and A. Ziv [3] proved that any sequence of 2n− 1 terms from an abelian group of order n contains an n-term zero-sum subsequence. This celebrated EGZ theorem is is an important result in combinatorial number theory and it has many different ge...

Around Pelikán’s conjecture on very odd sequences

Very odd sequences were introduced in 1973 by Pelikán who conjectured that there were none of length ≥ 5. This conjecture was disproved first by MacWilliams and Odlyzko [17] in 1977 and then by two different sets of authors in 1992 [1], 1995 [9]. We give connections with duadic codes, cyclic difference sets, levels (Stufen) of cyclotomic fields, and derive some new asymptotic results on the len...