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Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
Also, can you define you ordering more explicitly. Do you read words left-to-right or right-to-left?
Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
I don't think your comment above is helpful. I think it was appropriate to delete it.
Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
Isn't (3) already false for $w=101$, $u=10$ and $v=1$?
Nov
20
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
@TheMaskedAvenger This is definitely not what is going on. The modifications you are proposing would yield Lyndon words for the associated ordering. Nyldon words behave very differently. For example, the Nyldon words $101$ and $1011$ defy this kind of description.
Nov
18
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
@darijgrinberg: sorry, no. I was not saying that. I was just pointing out that things that seem to happen in a 2 letter alphabet are unlikely to be true for bigger alphabets. For example, certain palindromes are Nyldon, but cycling the first letter to the end will not make them Lyndon Honestly, these Nyldon words are baffling.
Nov
18
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
@PerAlexandersson, I don't think this coincidence in a 2 letter alphabet generalizes. The thing about Lyndon words is that they are filled with patterns. For example, every Lyndon work looks like $w=w_1^kw_1'i$, where $w_1$ is Lyndon, $w_1'$ is a (possibly empty) left factor of $w_1$ and $i$ is a letter such that $w_1'i>w_1$ (this was proved by Leclerc). In contrast, Nyldon words seem to be pattern avoiding.
Nov
7
comment Irreducible representations of Weyl group of F$_4$ on zero weight spaces?
I don't have Bourbaki with me. Is $\varpi_1$ short or long?
Nov
3
answered Given a locally nilpotent derivation over a field of characteristic 0 and a local slice, how is the ring homomorphism below defined?
Nov
2
comment When exactly and why matrix multiplication became a part of undergraduate curriculum?
Just to focus in, is your question about when US universities adopted linear algebra in their core curriculum? And, if this can be established, who were the advocates of this that made it happen?
Nov
1
answered The formula for a perhaps basic identity (move from stackexchange)
Oct
31
awarded  Yearling
Oct
22
answered Does Schur's Lemma hold in this case? Regular representations of $S_n$ over $\mathbb R$
Oct
18
revised Homomorphisms from irreducible spaces to reducible spaces
added 25 characters in body
Oct
18
answered Homomorphisms from irreducible spaces to reducible spaces
Oct
17
comment Shift-invariant symmetric functions in representation theory?
The permutation representation of $S_n$ is an $n$-dimensional vector space $V$ with basis $x_1,\ldots,x_n$. The symmetric algebra is the ring of symmetric functions in $n$-variables. The standard $n-1$ dimensional representation (call it $W$) is the subspace of $V$ with basis $x_i-x_{i+1}$. Now, $S(W)\subset S(V)$ consists of shift invariant symmetric functions.
Oct
9
comment Generators of invariant polynomials of semisimple Lie algebra
Wouldn't `Schur functions' be the canonical choice?
Oct
8
comment A class of matrix determinants between Wronskians and Vandermondes
are you specifically interested in equation (4.2) in the link? This seems much more tractable than the general problem.
Oct
8
comment A class of matrix determinants between Wronskians and Vandermondes
@Alex R. I seem to have added the assumption that $d_1=n-1$ in my answer. As you point out, it is much more complicated if this is not the case. I think that if $d_1=n+k-1$, then something like I wrote holds if $d_1-d_2=k_1+k$ (with $G=0$ for $>k_1+k)$.
Oct
8
revised A class of matrix determinants between Wronskians and Vandermondes
deleted 92 characters in body
Oct
7
answered A class of matrix determinants between Wronskians and Vandermondes