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May
14
comment Expected number of returns by time n in a symmetric 1-d random walk?
possible duplicate of Expected number of returns to zero in a symmetric random walk - closed form
May
13
comment Proving that $SL_2(\mathbb{Z}_5) / \{\pm I\}\simeq A_5$
cf. math.stackexchange.com/q/93762/152
May
6
comment Combinatorial definition of Hall–Littlewood polynomials (sum over SSYT?)
...but extracting something explicit for HL polynomials from that doesn't look like an easy task...
May
6
comment Combinatorial definition of Hall–Littlewood polynomials (sum over SSYT?)
Wikipedia page on Macdonald polynomials a) doesn't contain words 'semi-standard' or 'augmented'; b) doesn't give a combinatorial description of Macdonald polynomials — it mentions a description of transformed Macdonald polynomials that uses 'certain combinatorial statistics' inv and maj. I guess details can be found in arxiv.org/abs/math/0409538
Apr
10
comment A reference for a combinatorial identity
The second form looks like just a Vandermonde's identity ($\binom{i+k-1}i=\pm\binom{-k}i$ etc).
Apr
8
comment Stiefel-Whitney classes with Z-coefficients
(Re: The only problem I see is with the Steenrod square operation which may be undefined for integral coefficients) Well, yes there are no non-trivial stable operations from H(-;Q) to H(-;Q), after all...
Mar
31
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
@Stefan (Re: last comment) No-no, I want a counter example where X is not Hausdorff (and $Y$ is locally compact).
Mar
30
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
@user87690 Right, thank you (if one assumes a strong enough version of local compactness — for non-Hausdorff spaces there are different versions of the definition — one needn't assume that $Y$ is Hausdorff — I've updated the question).
Mar
30
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
@johndoe ...And Sierpinski set is, perhaps, a good choice for $Z$ — AFAIR, there is some theorem along the lines 'if the exponential law hold for $Z=\text{Sierpinski}$ it holds for all $Z$'.
Mar
30
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
...the idea of taking finite $X$ and $Y$ is quite tempting — because finite topological spaces are locally-compact (and I don't know many example of non-Hausdorff locally-compact spaces). I've tried to play with some examples — but haven't succeeded.
Mar
30
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
@johndoe Well, if either $X$, $Y$ or $Z$ is discrete the statement seems to be more or less obviously true. But slightly more generally...
Mar
30
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
Related (but not answering the question): @ n-Category Cafe
Mar
21
comment Combinatorial definition of Hall–Littlewood polynomials (sum over SSYT?)
@IgorMakhlin (И про t-версию Бриона и т.п. мы бы с М.Б. с интересом послушали в какой-то момент.)
Mar
21
comment Combinatorial definition of Hall–Littlewood polynomials (sum over SSYT?)
@IgorMakhlin О, привет. Well, yes and no: there is an explicit description of the $t$-weight $\psi$ in Macdonald's book — but it's complicated and not terribly satisfying. So if you have a better answer, please explain it (here or iRL).
Mar
12
comment Geometric interpretation for sum of fourth powers
Well, yes, $1^k+2^k+...+n^k$ is the value of an Ehrhart polynomial for the 'hybercubic pyramid'. But does this help to compute the sum?
Jan
30
comment Is reduced homology a full functor on connected spaces?
The question is about the category of connected spaces.
Jan
30
comment Is reduced homology a full functor on connected spaces?
Uh? $\tilde H(pt)=0$.
Jan
22
comment Curious Binomial Coefficient Identity
it's a (yet another) form of Vandermonde's identity
Jan
19
comment Binomial Identity $\sum\binom{2n+1}{2k+1}\binom{m+k}{2n} = \binom{2m}{2n}$
see also math.stackexchange.com/q/1107465 for a bijective proof of an equivalent identity
Jan
19
comment Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$
come to think of it, substituting $a\to 2n+1$, $n\to 2m-2n$ (and $k\to m-2n+k$) one can see that these two identities are equivalent