Zobrazeno 1 - 10
of 306
pro vyhledávání: '"Krattenthaler, Christian"'
Autor:
Albion, Seamus, Eisenkölbl, Theresia, Fischer, Ilse, Gangl, Moritz, Höngesberg, Hans, Krattenthaler, Christian, Rubey, Martin
We exhibit, for any positive integer parameter $s$, an involution on the set of integer partitions of $n$. These involutions show the joint symmetry of the distributions of the following two statistics. The first counts the number of parts of a parti
Externí odkaz:
http://arxiv.org/abs/2407.16043
We give a closed form for $quotients$ of truncated basic hypergeometric series where the base $q$ is evaluated at roots of unity.
Comment: $1+2+\dots+N = 1\cdot2\dotsb N$ pages
Comment: $1+2+\dots+N = 1\cdot2\dotsb N$ pages
Externí odkaz:
http://arxiv.org/abs/2406.02954
Publikováno v:
J. Symbol. Comput. 127 (2025), 102352
In his work on the twenty vertex model, Di Francesco [Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula for the e
Externí odkaz:
http://arxiv.org/abs/2401.08481
Autor:
Ciucu, Mihai, Krattenthaler, Christian
The original motivation for this paper goes back to the mid-1990's, when James Propp was interested in natural situations when the number of domino tilings of a region increases if some of its unit squares are deleted. Guided in part by the intuition
Externí odkaz:
http://arxiv.org/abs/2308.06863
Let $S=K[x_1,\ldots,x_n]$ be the ring of polynomials over a field $K$. Given two monomial ideals $0\subset I\subsetneq J \subset S$, we present a new method to compute the Hilbert depth of $J/I$. As an application, we show that if $u\in S$ is a monom
Externí odkaz:
http://arxiv.org/abs/2306.09450
Di Francesco introduced Aztec triangles as combinatorial objects for which their domino tilings are equinumerous with certain sets of configurations of the twenty-vertex model that are the main focus of his article. We generalize Di Francesco's const
Externí odkaz:
http://arxiv.org/abs/2305.01774
In [Ramanujan J. 52 (2020), 275-290], Romik considered the Taylor expansion of Jacobi's theta function $\theta_3(q)$ at $q=e^{-\pi}$ and encoded it in an integer sequence $(d(n))_{n\ge0}$ for which he provided a recursive procedure to compute the ter
Externí odkaz:
http://arxiv.org/abs/2304.11471
Autor:
Krattenthaler, Christian
We give bijective proofs using Fomin's growth diagrams for identities involving numbers of vacillating tableaux that arose in the representation theory of partition algebras or are inspired by such identities.
Comment: AmS-TeX; 24 pages. Error i
Comment: AmS-TeX; 24 pages. Error i
Externí odkaz:
http://arxiv.org/abs/2304.07657
The identities which are in the literature often called ``bounded Littlewood identities" are determinantal formulas for the sum of Schur functions indexed by partitions with bounded height. They have interesting combinatorial consequences such as con
Externí odkaz:
http://arxiv.org/abs/2301.13117
Autor:
Wang, Chen, Krattenthaler, Christian
The celebrated (First) Borwein Conjecture predicts that for all positive integers~$n$ the sign pattern of the coefficients of the ``Borwein polynomial'' $$(1-q)(1-q^2)(1-q^4)(1-q^5) \cdots(1-q^{3n-2})(1-q^{3n-1})$$ is $+--+--\cdots$. It was proved by
Externí odkaz:
http://arxiv.org/abs/2201.12415