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pro vyhledávání: '"Viennot, P."'
Autor:
Liu, Moxuan J.
Let $\mathbf{x}_{n \times n}$ be a matrix of $n \times n$ variables, and let $\mathbb{C}[\mathbf{x}_{n \times n}]$ be the polynomial ring on these variables. Let $\mathfrak{S}_{n,r}$ be the group of colored permutations, consisting of $n \times n$ co
Externí odkaz:
http://arxiv.org/abs/2401.07850
Akademický článek
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Autor:
Rhoades, Brendon
Let $\mathbf{x}_{n \times n}$ be an $n \times n$ matrix of variables and let $\mathbb{F}[\mathbf{x}_{n \times n}]$ be the polynomial ring in these variables over a field $\mathbb{F}$. We study the ideal $I_n \subseteq \mathbb{F}[\mathbf{x}_{n \times
Externí odkaz:
http://arxiv.org/abs/2306.08718
Autor:
Lee, Yi-Lin
Publikováno v:
Electron. J. Combin. 29 (2022), no. 2, Paper No. 2.41, 31 pp
Consider a weighted directed acyclic graph $G$ having an upward planar drawing. We give a formula for the total weight of the families of non-intersecting paths on $G$ with any given starting and ending points. While the Lindstr\"om-Gessel-Viennot th
Externí odkaz:
http://arxiv.org/abs/2112.06115
We give a direct proof of a result of Sundaram and Stanley: that the dimension of the space of invariant vectors in a $2k$-fold tensor product of the vector representation of $\mathfrak{sp}_{2n}$ equals the number of $(n+1)$-avoiding matchings of $2k
Externí odkaz:
http://arxiv.org/abs/2108.11528
Autor:
Xiong, Rui
In this article, we use Lindstr\"om Gessel Viennot Lemma to give a short, combinatorial, visualizable proof of the identity of Schur polynomials -- the sum of monomials of Young tableaux equals to the quotient of determinants. As a by-product, we hav
Externí odkaz:
http://arxiv.org/abs/2003.09215
Autor:
Brendon Rhoades
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
Let ${\mathbf {x}}_{n \times n}$ be an $n \times n$ matrix of variables, and let ${\mathbb {F}}[{\mathbf {x}}_{n \times n}]$ be the polynomial ring in these variables over a field ${\mathbb {F}}$ . We study the ideal $I_n \subseteq {\mathb
Externí odkaz:
https://doaj.org/article/e5d8cfce1267460684fb4f33aea47e4e
Autor:
Proctor, Robert A., Willis, Matthew J.
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 23 no. 1, Combinatorics (April 23, 2021) dmtcs:6632
Let $\lambda$ be a partition with no more than $n$ parts. Let $\beta$ be a weakly increasing $n$-tuple with entries from $\{ 1, ... , n \}$. The flagged Schur function in the variables $x_1, ... , x_n$ that is indexed by $\lambda$ and $\beta$ has bee
Externí odkaz:
http://arxiv.org/abs/1701.01182
Autor:
Víctor López
Publikováno v:
Ciències, Iss 45 (2023)
Laurence Viennot ha estat una investigora francesa pionera en la didàctica de la física, que ha tingut una gran influència al camp de la recerca en ensenyament de la física al nostre país. Arrel de la trista noticia de la seva mort el passat est
Externí odkaz:
https://doaj.org/article/a4c1ed23c94147349983e5ff81026a28
Grassmann (or anti-commuting) variables are extensively used in theoretical physics. In this paper we use Grassmann variable calculus to give new proofs of celebrated combinatorial identities such as the Lindstr\"om-Gessel-Viennot formula for graphs
Externí odkaz:
http://arxiv.org/abs/1604.06276