hardmath

Knoxville, TN

uclue.com

Age: 62

Enjoys programming in Prolog.

Richard O'Keefe: "Prolog is an efficient programming language because it is a very stupid theorem prover."

When I cross the street, I look both ways: up and dn.

5h
revised Counting 5-point, 4-edge subgraphs of a chess board
added a final total of 4483 subgraphs
8h
comment Add a link to the reputation tab from the profile page
In hindsight the "prototyping" of the new profile/activity tabs on Meta.SE did not give a realistic feel for how it would work with Community sites or their "child meta's". I'm still stumbling about for ways to navigate quickly, or in patterns that replaced my habitual movements.
8h
comment Asked a trivial question, got a simple answer,was put on hold. Should I delete it?
The specific Question at issue has now been reopened.
8h
comment Effect on existing roots of polynomial when adding small higher-order term
It sounds like by "accuracy" you have in mind the location of roots of the analytic function represented by the Taylor series. This is more difficult than showing the perturbation of "existing" roots is small by adding a "small" higher order term. Consider the exponential function $y = e^x$ and its truncations. At odd degrees truncations have one real root; at even degrees truncations have no real roots.
9h
revised Counting 5-point, 4-edge subgraphs of a chess board
added picture of the simple path configurations and some brief remarks
9h
revised Counting 5-point, 4-edge subgraphs of a chess board
clarified and narrowed the title
9h
comment Effect on existing roots of polynomial when adding small higher-order term
Are you asking about roots in the complex plane or real roots? In the complex plane we can prove that perturbations of the coefficients give continuous trajectories of the "existing" roots, but may cause real roots to appear or disappear (when multiplicity is more than one).
9h
revised Help In Learning Prolog
added quote from linked website
20h
reviewed Looks Good The number of $q$-Sylow subgroups cannot be $p$ for prime $p<q$
20h
comment Gauss Method to show
While it is that geometric series, it might be helpful to the OP to show how the series can be manipulated to give the result, e.g. multiplying the series by $x-y$ and subtracting.
2d
revised Counting 5-point, 4-edge subgraphs of a chess board
added missing degree 3 figure to picture; adjusted text, esp. to remove disconnected case
2d
comment Counting 5-point, 4-edge subgraphs of a chess board
We can simply drop the disconnected cases from the counts. When every vertex in a graph has the same degree, we say the graph is regular. Note that the chess board has many vertices of degree $4$, but vertices on the boundary of the board have degree $2$ or $3$, so these "grid" graphs are not regular.
2d
comment No Borel well-order of the reals?
Related: Is there a known well-ordering of the reals?
2d
revised Counting 5-point, 4-edge subgraphs of a chess board
noted missing degree 3 case and gave its counts prior to adding the picture
2d
reviewed Reopen Direct method in the calculus of variations
2d
revised Counting 5-point, 4-edge subgraphs of a chess board
added diagram of maximum degree 3 sequences and counts of each of four cases
2d
comment there is a unitary $U \in {M_m}$ such that $X = YU$. Why $X$ and $Y$ have the same range?
A direct way to approach this, using the invertibility of $U$, is to show each column of $X$ belongs to the column space of $Y$ (evident) and each column of $Y$ belongs to the column space of $X$ (a bit of algebra is needed).
2d
revised Counting 5-point, 4-edge subgraphs of a chess board
math and other formatting improvements/punctuation
2d
comment Counting 5-point, 4-edge subgraphs of a chess board
A similar kind of Question, restricted to counting non-crossing "rope" paths between two points, was proposed here: How many possibilities to arrange a rope of length $n$ between two points?. The poster of that Question was also disappointed to learn there would be no exact formula, though as I pointed out in my response, if self-intersections were allowed, it would make the counting easier.
2d
comment Counting 5-point, 4-edge subgraphs of a chess board
How about the property of being connected? Did you want to include the disconnected $p$-point, $t$-edge subgraphs in your count?
1 2 3 4 5