Главная

Donald M. Davis

  1. Coefficients in powers of the log series.

    Втр, 01/19/2010 - 16:01 — SomNambul
    Authors: Donald M. Davis
    Subjects: Number Theory
    Abstract

    We determine the p-exponent in many of the coefficients in the power series
    (log(1+x)/x)^t, where t is any integer. In our proof, we introduce a variant of
    multinomial coefficients. We also characterize the power series x/log(1+x) by
    certain zero coefficients in its powers.

  2. Maximizing a combinatorial expression arising from crowd estimation.

    Пнд, 11/02/2009 - 16:01 — SomNambul
    Authors: Donald M. Davis
    Subjects: Combinatorics
    Abstract

    We determine, within 1, the value of N for which sum (s1 choose i)(s2 choose
    N)(s1 choose N-i)(N choose i) achieves its maximum value. Here s1 and s2 are
    fixed integers. This problem arises in studying the most likely value for the
    size of the union of A, B, and C if A and C are disjoint sets of size s1, and B
    is a set of size s2. Attempting to remove the 1 unit of indeterminacy leads to
    interesting conjectures about a family of rational functions.

Math-arch

RSS-материал