bio | website | jamespropp.org |
---|---|---|
location | ||
age | ||
visits | member for | 5 years, 2 months |
seen | 6 hours ago | |
stats | profile views | 2,241 |
I am interested in combinatorics, probability, dynamical systems, and various other topics.
Mar 21 |
comment |
How exactly does Schützenberger promotion relate to Striker-Williams promotion?
Jessica and I discussed our respective approaches in person yesterday, and we feel that they're quite different. Jessica's answer treats standard tableaux; my answer (which appears below) treats semistandard tableaux. Her tableaux have only two rows; mine can have any number of rows. Her tableaux can be skew; mine must be non-skew, and indeed must be rectangular. She associates tableaux with order ideals in subposets of root posets of type A (triangles); I associate tableaux with points in the order polytope of minuscule posets of type A (rectangles). |
Mar 16 |
revised |
How exactly does Schützenberger promotion relate to Striker-Williams promotion?
added 1 character in body |
Mar 13 |
revised |
How exactly does Schützenberger promotion relate to Striker-Williams promotion?
added 763 characters in body |
Mar 10 |
comment |
slick-proof-of-trick-for-counting-domino-tilings
Nice; I'll definitely include this proof the next time I teach a course on perfect matchings! (Though I am a bit fuzzy on how one would prove the topological lemma that asserts that these four kinds of singularities are all that can happen.) |
Mar 9 |
revised |
Modeling bubble rafts
deleted 191 characters in body |
Mar 2 |
comment |
Why does the Riemann zeta function have non-trivial zeros?
Pace Nielsen's question deserves a more serious answer. Here is a paraphrase David Hansen might prefer: What concrete number-theoretic phenomena allow one to "see" the influence of 14.1...? Barry Mazur, at the end of "A Lecture on Primes" (msri.org/general_events/20798), alluded to the existence of such phenomena; can anyone provide details? |
Mar 2 |
comment |
Regularized sums of Mobius sequence
Is there some sort of asymptotic expansion for $M(x)$ in which (a) the constant term is $-2$, (b) the other terms correspond to roots of $\zeta$ on the critical line, and (c) the constant term dominates the other terms when $x >> 10^{-10}$? That would explain why it misleadingly seems to be converging to $-2$, and would reinforce Lucia's point that the zeroes are the reason for the non-convergence. |
Mar 2 |
comment |
Regularized sums of Mobius sequence
For anyone who's interested in knowing just how small $\Gamma(1/2+14.1\dots i)$ is, Mathematica reports that its real and imaginary parts are on the order of $10^{-10}$. |
Mar 2 |
comment |
Regularized sums of Mobius sequence
@Lucia: I think your response settles my first two questions, but what about the third? I know that the Dirichlet series converges when Re $s > 1$, but I don't know whether the full domain of convergence includes some values of $s$ with Re $s \leq 1$ (such as real numbers strictly between 0 and 1). |
Mar 1 |
asked | Regularized sums of Mobius sequence |
Feb 24 |
comment |
Distinguishing combinatorial maps by their linearizations
I don't understand how one can get away with ignoring the cycles completely. What if there are nothing but cycles? That is, what if the original combinatorial map is a permutation? Then we know that spectrum of the associated linear map is $GL(n)$-invariant, and the spectrum determines the cycle-structure. |
Feb 23 |
accepted | Distinguishing combinatorial maps by their linearizations |
Feb 23 |
comment |
Distinguishing combinatorial maps by their linearizations
I don't quite see how to reconcile this with the criterion of Saks and Gansner described by Stanley (below). Taking $n=4$ and $j=2$, I find that for the idempotent that maps 1 to 1 and maps 2, 3, and 4 to 2, the largest number of vertices in a union of two paths is 3, while for the idempotent that maps 2 and 4 to 2 and maps 1 and 3 to 1, the largest number of vertices in a union of two paths is $4 \neq 3$. What am I missing? |
Feb 22 |
asked | Distinguishing combinatorial maps by their linearizations |
Feb 19 |
revised |
Is the Ford disk packing optimal?
deleted 328 characters in body |
Feb 19 |
accepted | Is the Ford disk packing optimal? |
Feb 19 |
answered | Is the Ford disk packing optimal? |
Feb 18 |
awarded | Citizen Patrol |
Feb 18 |
asked | Modeling bubble rafts |
Feb 18 |
revised |
Is the Ford disk packing optimal?
added 328 characters in body |