DSpace Collection:http://hdl.handle.net/123456789/422024-03-29T15:47:00Z2024-03-29T15:47:00ZRamseyan variations on symmetric subsequencesVerbitsky, Oleghttp://hdl.handle.net/123456789/542020-01-24T21:27:49Z2002-12-13T00:00:00ZTitle: Ramseyan variations on symmetric subsequences
Authors: Verbitsky, Oleg
Description: A theorem of Dekking in the combinatorics of
words implies that there exists an injective order-preserving transformation
f : {0, 1, . . . , n} → {0, 1, . . . , 2n} with the restriction
f(i + 1) ≤ f(i) + 2 such that for every 5-term arithmetic progression
P its image f(P) is not an arithmetic progression. In this paper
we consider symmetric sets in place of arithmetic progressions
and prove lower and upper bounds for the maximum M = M(n)
such that every f as above preserves the symmetry of at least one
symmetric set S ⊆ {0, 1, . . . , n} with |S| ≥ M.2002-12-13T00:00:00ZAn additive divisor problem in Z[i]Savasrtu, O. V.Varbanets, P. D.http://hdl.handle.net/123456789/532020-01-24T21:27:29Z2003-02-22T00:00:00ZTitle: An additive divisor problem in Z[i]
Authors: Savasrtu, O. V.; Varbanets, P. D.2003-02-22T00:00:00ZUniform ball structuresProtasov, I. V.http://hdl.handle.net/123456789/522020-01-24T21:26:47Z2003-01-31T00:00:00ZTitle: Uniform ball structures
Authors: Protasov, I. V.
Description: A ball structure is a triple B = (X, P,B), where
X, P are nonempty sets and, for all x ∈ X, ® ∈ P, B(x, ®) is a subset
of X, x ∈ B(x, ®), which is called a ball of radius ® around x.
We introduce the class of uniform ball structures as an asymptotic
counterpart of the class of uniform topological spaces. We show
that every uniform ball structure can be approximated by metrizable
ball structures. We also define two types of ball structures
closed to being metrizable, and describe the extremal elements in
the classes of ball structures with fixed support X.2003-01-31T00:00:00ZPrincipal quasi-ideals of cohomological dimension 1Novikov, B. V.http://hdl.handle.net/123456789/512020-01-24T21:27:40Z2003-02-10T00:00:00ZTitle: Principal quasi-ideals of cohomological dimension 1
Authors: Novikov, B. V.
Description: We prove that a principal quasi-ideal of a noncommutative
free semigroup has cohomological dimension 1 if and
only if it is free.2003-02-10T00:00:00Z