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Jun
20
reviewed Close Why is combinatorics not a part of the Tripos?
Jun
20
reviewed Close Maximum value of trigonometric expression
Jun
20
answered Combinatorial Interpretation of these two identities
Jun
20
answered Alternative way to count the number of solutions to the equation $x^2 + y^2 = -1$ over $\Bbb Z /p$
Jun
20
comment Recurrence $(n+2)\text{Cat}_{n+1}=(4n+2)\text{Cat}_n$ for non-crossing matchings
Understanding is its own reward.
Jun
19
reviewed Reviewed matrix inequality proof [completion of squares]
Jun
17
comment Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
See also an example of using Jacobi sums to count points on $y^2=x^3-x$.
Jun
17
revised Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
P.S. about Weil etc
Jun
17
answered Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
Jun
16
awarded  Nice Answer
Jun
15
reviewed Close Is being positive and orthogonal sufficient for being identity?
Jun
15
comment Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
1) «Rational parametrization of conics»; 2) «Jacobi sums».
Jun
15
revised $SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong \mathbb A_4$
edited tags
Jun
15
comment $SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong \mathbb A_4$
From geometric POV the homomorphism to $A_4$ comes from the action of $SL_2(\mathbb Z_3)$ on 4-element set $P^1(\mathbb Z_3)$ (by fractional-linear transformations, if you will). Cf. $PSL_2(\mathbb F_4)\cong A_5$ etc.
Jun
7
comment Proof of $\sum_{n=1}^\infty \frac{1}{n^4 \binom{2n}{n}}=\frac{17\pi^4}{3240}$
related: math.stackexchange.com/q/144985
Jun
4
comment Why universal G-bundles are contractible?
If $B$ represents the functor «$X$ → principal $G$-bundles on $X$», then $E$ represents the functor «$X$ → principal $G$-bundles on $X$ with a fixed section». This functor is trivial, so $E$ is contractible.
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