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answered Catalan numbers as sums of squares of numbers in the rows of the Catalan triangle - is there a combinatorial explanation?
May
22
comment How long can a cycle of antichains in a finite partial order be?
Readers of my previous comment should realize that what I call $L_X$ has been changed in the question to $Q_X$.
May
21
comment How long can a cycle of antichains in a finite partial order be?
The bijection $L_X$ is well-known and appears in many papers. (You seem to be using $L_X$ in two different ways.) It has been called the Fon-der-Flaass action, the Panyushev action, and rowmotion. One reference is arxiv.org/pdf/1108.1172v3.pdf. However, I don't know of any work directly relevant to the question here.
May
17
comment Uniform generation of Symmetric Plane Partitons
From what set of symmetric plane partitions do you want to choose a random one?
May
13
comment I need to refind a reference on multigraded Hilbert series
The proof of Theorem 11.1 in Atiyah and Macdonald, Introduction to Commutative Algebra, carries over to the multigraded case. It is also an easy consequence of the Hilbert syzygy theorem.
May
12
comment Interesting applications of the Pigeon-hole Principle
I have reposted this at math.mit.edu/~rstan/pigeon.pdf.
May
6
comment Combinatorial polynomials from general diagram fillings?
For so-called %-avoiding diagrams, see the paper by Reiner and Shimozono at citeseerx.ist.psu.edu/viewdoc/….
Apr
30
comment Number of matrices with given Smith normal form
Yinghui Wang has just written a paper on this topic. Soon it should be posted on the arXiv.
Apr
29
awarded  Good Answer
Apr
28
answered Residue for the generating function of the Euler totient function
Apr
27
comment Generalization of Schur polynomials
There are some listed on page 405 of Enumerative Combinatorics, vol.2, that don't seem to be on your list.
Apr
25
comment A digraph related to permutations
One reason that the number of Hamiltonian cycles divided by $(n-1)!^{(n-1)!}$ factors quite a bit is the $S_n$-symmetry. A similar situation is at OEIS oeis.org/A120061. See also Chapter 10, Exercise 7(d) of my book Algebraic Combinatorics.
Apr
25
comment Is anything known about the eigenspectrum of the regular representation of the permutation group?
@Anirbit: Stembridge's Theorem 3.3 gives a combinatorial formula for the eigenvalues. The characters of $S_n$ are not involved.
Apr
25
comment A question on (odd) perfect numbers
You left out the essential condition that $k$ is odd.
Apr
25
answered Is anything known about the eigenspectrum of the regular representation of the permutation group?
Apr
24
comment A digraph related to permutations
Continuation of previous comment: $02167802121430577869247906928263206218129022043438732817393$ $78238299321477251081703396523732122511001097003078223354740$ $21115543570842542767571682953869289112205514506240000000000000000000$. This must have a large prime factor since Maple has been taking many hours trying to factor it.
Apr
24
comment A digraph related to permutations
For $n=7$ the number is $6!^{720}\cdot 176183413608273968258307195020261201995935498443817037880077$ $33015680734978977985994540951427241494888517320111715796104$ $01678883391824293568187890362411864333732042160720070054426$ $13973761520215432676342816642484823001649942753538184971817$ $00932653194251714270416078406552688838875907139437076885891$ $46604444975789292489211082309639859152636172062362845942377$ $16134182843447651691194901389583522511049879097164330759592530013$ (continued on next comment)
Apr
23
comment A digraph related to permutations
For $n =6$ the number is $5!^{120}\cdot 2^{32}\cdot 3^{29} \cdot 5^{20}\cdot 7^9\cdot 23\cdot 37^3\cdot 53\cdot 79\cdot 83\cdot 311^9\cdot 1993\cdot 5569\cdot 57679$.
Apr
23
comment A digraph related to permutations
For $n=5$ the number of Hamiltonian cycles is $4!^{24}\cdot 2^{11}\cdot 3^5\cdot 5^6\cdot 13^2\cdot 17\cdot 47$.