Richard Stanley
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Registered User
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1d |
answered | Why are the dinv-statistic and the partition length equidistributed? |
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May 17 |
revised |
how to proof this Stirling related equation corrected spelling of Stirling |
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May 16 |
awarded | ● Stellar Question |
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May 9 |
comment |
Discrete disjoint covering of integer lattices For any $n\times n$ integer matrix $M$ with determinant $d\neq 0$ and columns $v_1,\dots,v_n$, there are exactly $|d|-1$ nonzero integer vectors $u_1,\dots,u_{d-1}$ of the form $u_i=\sum a_i v_i$, where $0\leq a_i<1$. The point here is that these nonzero $u_i$'s should form a basis for the lattice $\mathbb{Z}^n$. |
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May 9 |
answered | Discrete disjoint covering of integer lattices |
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May 7 |
accepted | Semi-Standard Young Diagrams and Families |
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May 7 |
answered | Semi-Standard Young Diagrams and Families |
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Apr 28 |
awarded | ● Nice Answer |
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Apr 25 |
comment |
Inequivalence of group representations preserved under tensor product? If $r_1$ and $r_2$ are two ordinary linear representations of the same degree of a finite group $G$ and $R$ is the regular representation, then $r_1\otimes R\cong r_2\otimes R$. |
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Apr 24 |
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Using extended group rings for combinatorial generating functions Guoce Xin has some papers that seem relevant. See for instance front.math.ucdavis.edu/0409.5190 and front.math.ucdavis.edu/0504.5425. |
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Apr 10 |
comment |
Criteria for ghost-Witt vectors: looking for history and references Some partial information (with references) can be found in Exercise 5.2 of Enumerative Combinatorics, vol. 2. |
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Apr 9 |
accepted | Relations involving Stirling numbers of second kind |
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Apr 9 |
answered | Relations involving Stirling numbers of second kind |
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Apr 5 |
comment |
Access to a preprint by D. N. Verma The above formula can be simplified to $$ \frac 12\sum_{j=0}^{m-1}(m-j)^{n-3}(-1)^{j+1}\binom nj. $$ |
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Mar 27 |
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Other Variant of Schur Polynomials/Functions Ignoring your list of properties, there is a list of some variants of Schur functions (with references) in the Notes to Chapter 7 of my book Enumerative Combinatorics, vol. 2. |
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Mar 21 |
comment |
Counting seating arrangements at a circular table Do the members of a team sit together with no spaces between them? In your example, since the boys are identical it seems to me that there is only one way of seating two teams of two and one way of seating a team of three and a team of one, so two ways in all. |
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Mar 21 |
answered | Counting linear extensions of unlabeled series parallel structures |
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Mar 19 |
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Characters of p-groups In fact, if $M$ is the number of nonlinear irreducible characters, then $M\equiv 0$ (mod $p^2-1$) if $n\equiv r$ (mod 2); $M\equiv p-1$ (mod $p^2-1$) if $n$ is odd and $r$ is even; and $M\equiv -p+1$ (mod $p^2-1$) if $n$ is even and $r$ is odd. |
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Mar 19 |
accepted | Characters of p-groups |
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Mar 18 |
answered | Characters of p-groups |
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Mar 16 |
answered | Generalization’s of Greene’s Theorem for the Robinson-Schensted correspondence |
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Mar 8 |
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Invertibility of a certain matrix indexed by the Hamming cube The solution to Exercise 3.96(a) shows how the matrix $M=F(s\wedge t,s)$ can be triangularized, from which a recurrence for the entries of $M$ follows. I believe this is essentially what is done in Section 6 of arXiv:1110.4954, though I haven't looked at this very carefully. It would be interesting to find an explicit formula for the entries of $M^{-1}$. |
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Mar 8 |
answered | Invertibility of a certain matrix indexed by the Hamming cube |
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Mar 2 |
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Access to a preprint by D. N. Verma I would like to thank Yannic Vargas, who located a copy of Verma's paper in the LACIM library and emailed me a scanned file. |
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Mar 1 |
awarded | ● Nice Question |
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Feb 28 |
comment |
Access to a preprint by D. N. Verma Thanks, this is very helpful. For $n=2m$ I get the formula $$ \frac 12\sum_{j=0}^{m-1}(m-j)^{n-3}(-1)^{j+1}{n\choose j} (2j-n+1). $$ Assuming that my sequence and Verma's are the same (which must be true), then this gives a simpler formula than in the reference you provide. |
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Feb 28 |
asked | Access to a preprint by D. N. Verma |
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Feb 21 |
revised |
Good books on problem solving / math olympiad broken link fixed |
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Feb 18 |
accepted | Statistics on Lehmer codes |
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Feb 18 |
answered | Statistics on Lehmer codes |
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Feb 16 |
answered | What is the probability for sequence of lenght L in subset of [n] |
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Feb 15 |
accepted | Partial order relation on subsets |
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Feb 14 |
answered | Partial order relation on subsets |
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Feb 9 |
comment |
quotients of polynomial rings If the ideal $I$ is generated by homogeneous polynomials, then the condition is that $I$ is generated by polynomials of degree one. |
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Feb 9 |
revised |
quotients of polynomial rings missing ] inserted |
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Feb 6 |
awarded | ● Nice Answer |
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Jan 25 |
comment |
Is there a characterization of hyperplane arrangement intersection posets? Just the question of when a geometric lattice is the intersection lattice of a linear hyperplane arrangement is quite complicated. It is equivalent to asking when a matroid can be represented over a field. |
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Jan 22 |
answered | connected components of a real hyperplane arrangement |
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Jan 19 |
awarded | ● Good Question |
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Jan 15 |
answered | Elementary applications of linear algebra over finite fields |
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Jan 13 |
awarded | ● Popular Question |
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Jan 8 |
awarded | ● Nice Question |
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Jan 5 |
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A question on the Laurent phenomenon @quid: not at all. Thanks for doing this. |
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Jan 5 |
asked | A question on the Laurent phenomenon |
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Jan 4 |
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power of adjacency matrix It is highly unlikely that there is any simple computation to decide whether there is a path of length $\ell$ between two vertices (much less count how many such paths there are), since the existence of a path of length $p-1$, where $G$ has $p$ vertices, is NP-complete. |
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Dec 30 |
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Graph of $S_n$ with respect to transposition The graph $G_n$ is the Hasse diagram of the absolute order on $S_n$. This gives some insight into what this graph "looks like." See arxiv.org/pdf/0706.1405v2.pdf. |
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Dec 22 |
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Reconstructing the argument that yields Graham’s number Though irrelevant to Tim's question, Graham's number is small potatoes compared to some of the numbers cooked up by Harvey Friedman, e.g., his paper Long finite sequences, JCT(A) 95 (2001), 102-144. |
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Dec 22 |
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Any non-conforming numbers? Every integer is of the form $x^2-y^2$ or $x^2-y^2+1$, and thus of the form $x^2-y^2+z^p$ for any $p$ (where we can take $z=0$ or $z=1$), so you need to rule out this situation. |
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Dec 21 |
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Reference: Finite $p$-Groups The book Enumeration of Finite Groups by Blackburn, Neumann, and Venkataraman has a lot of information on $p$-groups. |
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Dec 21 |
accepted | Are there any binomial poset which has non-isomorphic interval of the same length? |
