Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Aigner, Florian"'
Autor:
Schreier-Aigner, Florian
The (dual) Cauchy identity has an easy algebraic proof utilising a commutation relation between the up and (dual) down operators. By using Fomin's growth diagrams, a bijective proof of the commutation relation can be "bijectivised" to obtain RSK like
Externí odkaz:
http://arxiv.org/abs/2404.04014
We introduce a probabilistic generalization of the dual Robinson--Schensted--Knuth correspondence, called $qt$RSK${}^*$, depending on two parameters $q$ and $t$. This correspondence extends the $q$RS$t$ correspondence, recently introduced by the auth
Externí odkaz:
http://arxiv.org/abs/2403.16243
Publikováno v:
European Journal of Combinatorics 122 (2024), 104000
The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi-Trudi formula and the Lascoux-Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of the symplec
Externí odkaz:
http://arxiv.org/abs/2305.11730
Arrowed Gelfand-Tsetlin patterns have recently been introduced to study alternating sign matrices. In this paper, we show that a $(-1)$-enumeration of arrowed Gelfand-Tsetlin patterns can be expressed by a simple product formula. The numbers are a on
Externí odkaz:
http://arxiv.org/abs/2302.04164
Autor:
Schreier-Aigner, Florian
We introduce a symmetry class for higher dimensional partitions - fully complementary higher dimensional partitions (FCPs) - and prove a formula for their generating function. By studying symmetry classes of FCPs in dimension 2, we define variations
Externí odkaz:
http://arxiv.org/abs/2301.12272
Autor:
Dequêne, Benjamin, Frieden, Gabriel, Iraci, Alessandro, Schreier-Aigner, Florian, Thomas, Hugh, Williams, Nathan
Although both noncrossing partitions and nonnesting partitions are uniformly enumerated for Weyl groups, the exact relationship between these two sets of combinatorial objects remains frustratingly mysterious. In this paper, we give a precise combina
Externí odkaz:
http://arxiv.org/abs/2212.14831
Autor:
Aigner, Florian, Fischer, Ilse
We introduce a new family $\mathcal{A}_{n,k}$ of Schur positive symmetric functions, which are defined as sums over totally symmetric plane partitions. In the first part, we show that, for $k=1$, this family is equal to a multivariate generating func
Externí odkaz:
http://arxiv.org/abs/2201.13142
Publikováno v:
In European Journal of Combinatorics August 2024 120
Publikováno v:
In European Journal of Combinatorics December 2024 122
Autor:
Aigner, Florian, Fischer, Ilse
There is the same number of $n \times n$ alternating sign matrices (ASMs) as there is of descending plane partitions (DPPs) with parts no greater than $n$, but finding an explicit bijection is an open problem for about $40$ years now. So far, quadrup
Externí odkaz:
http://arxiv.org/abs/2106.11568