http://hdl.handle.net/123456789/42 Thu, 16 Apr 2026 01:30:17 GMT 2026-04-16T01:30:17Z http://hdl.handle.net/123456789/54 Ramseyan variations on symmetric subsequences Verbitsky, Oleg 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. Fri, 13 Dec 2002 00:00:00 GMT http://hdl.handle.net/123456789/54 2002-12-13T00:00:00Z http://hdl.handle.net/123456789/53 An additive divisor problem in Z[i] Savasrtu, O. V.; Varbanets, P. D. Sat, 22 Feb 2003 00:00:00 GMT http://hdl.handle.net/123456789/53 2003-02-22T00:00:00Z http://hdl.handle.net/123456789/52 Uniform ball structures Protasov, I. V. 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. Fri, 31 Jan 2003 00:00:00 GMT http://hdl.handle.net/123456789/52 2003-01-31T00:00:00Z http://hdl.handle.net/123456789/51 Principal quasi-ideals of cohomological dimension 1 Novikov, B. V. We prove that a principal quasi-ideal of a noncommutative free semigroup has cohomological dimension 1 if and only if it is free. Mon, 10 Feb 2003 00:00:00 GMT http://hdl.handle.net/123456789/51 2003-02-10T00:00:00Z