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71.
Some functions defined on the set of integer triangular matrices and their modifications are considered. These functions are analogs of the classical determinant and permanent functions and provide a powerful apparatus for studying sequences generated by linear recursive equations. Modifications of these functions are used to solve the problem about trajectories on Ferre diagrams and to establish new combinatorial identities. 相似文献
72.
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75.
We discuss a dual of the Open Coloring Axiom introduced by Abraham et al. [U. Abraham, M. Rubin, S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of 1-dense real order types, Ann. Pure Appl. Logic 29 (2) (1985) 123–206] and show that it follows from a statement about continuous colorings on Polish spaces that is known to be consistent. We mention some consequences of the new axiom and show that implies that all cardinal invariants in Cichoń’s diagram are at least 2. 相似文献
76.
We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function
n2log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show
that n2log n is the smallest Dehn function of a multiple HNN extension of a free group with undecidable conjugacy problem.
Both authors were supported in part by the NSF grants DMS 0245600 and DMS 0455881. In addition, the research of the first
author was supported in part by the Russian Fund for Basic Research 05-01-00895, the research of the second author was supported
in part by the NSF grant DMS 9978802 and the US-Israeli BSF grant 1999298.
Received: February 2005; Revision: September 2005; Accepted: September 2005 相似文献
77.
Ben McCarty 《Topology and its Applications》2012,159(1):162-174
For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number. 相似文献
78.
79.
An analytic function of several variables is considered. It is assumed that the function vanishes at some point. According to the Weierstrass preparation theorem, in the neighborhood of this point the function can be represented as a product of a nonvanishing analytic function and a polynomial in one of the variables. The coefficients of the polynomial are analytic functions of the remaining variables. In this paper we construct a method for finding the nonvanishing function and the coefficients of the polynomial in the form of Taylor series whose coefficients are found from an explicit recursive procedure using the derivatives of the initial function. As an application, an explicit formula describing a bifurcation diagram locally up to second-order terms is derived for the case of a double root. 相似文献
80.
Yoshiko Sakata Mitsuyuki Ochiai Kayo Satoh 《Proceedings of the American Mathematical Society》2001,129(2):559-566
We will give a very simple algorithm to decompose a gluing homeomorphism of a planar Heegaard diagram of genus two into Dehn twists associated with the canonical base.