Problem Set #1 - University of Chicago Math

... B. Prove that the bound is sharp (i.e., it gives the exact number of topologies) if and only if N ≤ 2. ...

... B. Prove that the bound is sharp (i.e., it gives the exact number of topologies) if and only if N ≤ 2. ...

Exercises - Stanford University

... (1) Let R be a reduced commutative ring (no nonzero nilpotent elements). Classify all 1-dimensional commutative formal group laws over R which are polynomials. b a or G b m. (2) Give an example of a 1-dim polynomial group law over Z[]/2 which is not G (3) Show that formal group laws over R have fo ...

... (1) Let R be a reduced commutative ring (no nonzero nilpotent elements). Classify all 1-dimensional commutative formal group laws over R which are polynomials. b a or G b m. (2) Give an example of a 1-dim polynomial group law over Z[]/2 which is not G (3) Show that formal group laws over R have fo ...

The ring of formal power series

... power series designated by the same expression, and it often suffices to give a meaning to infinite sums and products, or other kinds of limits that one wishes to use to designate particular formal power series. It can however happen occasionally that one wishes to use a coarser topology, so that ce ...

... power series designated by the same expression, and it often suffices to give a meaning to infinite sums and products, or other kinds of limits that one wishes to use to designate particular formal power series. It can however happen occasionally that one wishes to use a coarser topology, so that ce ...

Cambridge University Press Richard P. Stanley

... subsumes the previous two, as well as method 5, which follows. Any counting function likely to arise in practice can be computed from an algorithm, so the acceptability of this method will depend on the elegance and performance of the algorithm. In general, we would like the time that it takes the a ...

... subsumes the previous two, as well as method 5, which follows. Any counting function likely to arise in practice can be computed from an algorithm, so the acceptability of this method will depend on the elegance and performance of the algorithm. In general, we would like the time that it takes the a ...

PDF

... formulas for recursively described sequences; this is known as the method of generating functions and will be illustrated below. We start with a commutative ring R. We want to define the ring of formal power series over R in the variable X, denoted by R[[X]]; each element P∞ of this ring can be writ ...

... formulas for recursively described sequences; this is known as the method of generating functions and will be illustrated below. We start with a commutative ring R. We want to define the ring of formal power series over R in the variable X, denoted by R[[X]]; each element P∞ of this ring can be writ ...

3. Formal power series are just sequences of

... ring of formal power series “of letter z” is C[[z]]. Sometimes a power series (2) is called a generating function of the sequence (an ), and the numbers a0 , a1 . . . are called coefficients of F . We stress that the signs + and Σ have in general no meaning for infinite sums. Neither the symbols z n ...

... ring of formal power series “of letter z” is C[[z]]. Sometimes a power series (2) is called a generating function of the sequence (an ), and the numbers a0 , a1 . . . are called coefficients of F . We stress that the signs + and Σ have in general no meaning for infinite sums. Neither the symbols z n ...