# Questions tagged [algebraic-combinatorics]

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### Canon in algebraic combinatorics and how to study

1) In subjects such as algebraic geometry, algebraic topology there is a very basic standard canonical syllabus of things one learns in order to get to reading research papers. Is there a similar ...
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### Algebraic ode of exponential generating series

Let $G(z)$ be a rational function. So if we have a series $$S(x):=\sum_{n}a_n x^n$$ where $$a_n = \prod_{i=1}^{n}G((i-1)h)$$ We can conclude that the series satisfies a Linear differential ...
2answers
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### A special class of weighted Motzkin paths

Consider Motzkin paths with the following weight: All up-steps and the horizontal steps on height $0$ have weight $1$, all down-steps have weight $t$ and the horizontal steps on even heights have ...
1answer
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### $2$-adic valuation of Schur $P$-functions in the power-sum basis

For a partition $\lambda$, let $P_\lambda$ be the Schur $P$-functions (case $t=-1$ of Hall-Littlewood symmetric functions) and let $p_\lambda=p_{\lambda_1}p_{\lambda_1}\cdots p_{\lambda_k}$ be the ...
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### Geometric or combinatorial interpretations of the (weak) Bruhat order?

$\DeclareMathOperator\Inv{Inv}$The weak Bruhat order on the symmetric group has a straightforward combinatorial interpretation: Consider a set of labelled balls $1,2,\dotsc,n$. Then for two ...
1answer
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### $B_k[1]$ sets with smallest possible $m = \max B_k[1]$ for given $k$ and $n = \lvert B_k[1]\rvert$ elements

Sidon sets are sets $A \subset \mathbb{N}$ such that for all $a_j,b_j \in A$ holds $$a_1+a_2=b_1+b_2 \iff \{a_1,a_2\}=\{b_1,b_2\}.$$ Thus if you know the sum of two elements, you know which elements ...
2answers
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1answer
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### What is a toric lattice? [closed]

What is a toric lattice? and how can I construct one in Macaulay2 and compute its basis? is there any alternative method to make one? Since I went through the whole ...
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### Minimizing coefficients in a product related to the Rogers Ramanujan identity

Start with the product for partitions into parts congruent to $1$ or $4$ modulo $5$: $(1 + x + x^2 + x^3 + ...)(1 + x^4 + x^8 + x^{12} +...)(1 + x^6 + x^{12} + x^{18} +...)$... Now replace some of the ...