Browsing 1  Oberwolfach Preprints (OWP) by MSC "05"
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Birational Rowmotion on a Rectangle over a Noncommutative Ring
[OWP202217] (Mathematisches Forschungsinstitut Oberwolfach, 20220920)We extend the periodicity of birational rowmotion for rectangular posets to the case when the base field is replaced by a noncommutative ring (under appropriate conditions). This resolves a conjecture from 2014. The proof ... 
Cataland: Why the Fuß?
[OWP201901] (Mathematisches Forschungsinstitut Oberwolfach, 20190121)The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known FußCatalan generalizations. ... 
Characterization of Tropical Planar Curves up to Genus Six
[OWP202206] (Mathematisches Forschungsinstitut Oberwolfach, 20220316)We provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six. 
A Cheeger Type Inequality in Finite Cayley Sum Graphs
[OWP201921] (Mathematisches Forschungsinstitut Oberwolfach, 20190731)  (5 May  27 July 2019)Let $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $S = d$. We show that if the undirected Cayley sum graph $C_{\Sigma}(G,S)$ is an expander graph and is nonbipartite, then the spectrum of its ... 
A Deformed Quon Algebra
[OWP201811] (Mathematisches Forschungsinstitut Oberwolfach, 20180625)The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and ... 
Matchings and Squarefree Powers of Edge Ideals
[OWP201925] (Mathematisches Forschungsinstitut Oberwolfach, 20191111)Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such ... 
New representations of matroids and generalizations
[OWP201118] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This ... 
On CoMinimal Pairs in Abelian Groups
[OWP201919] (Mathematisches Forschungsinstitut Oberwolfach, 20190709)A pair of nonempty subsets $(W,W')$ in an abelian group $G$ is a complement pair if $W+W'=G$. $W'$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \forall \,w'\in W'$. In general, given an arbitrary subset ... 
On Concentrators and Related Approximation Constants
[OWP201314] (Mathematisches Forschungsinstitut Oberwolfach, 20130610)Pippenger ([Pip77]) showed the existence of (6m, 4m, 3m, 6)concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m, 4m, 3m, 5.05)concentrator (which ... 
On the Gauss Algebra of Toric Algebras
[OWP201807] (Mathematisches Forschungsinstitut Oberwolfach, 20180425)Let $A$ be a $K$subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\mathbb{G}(A)$ of $A$ is generated by monomials of ... 
On the Invariants of the Cohomology of Complements of Coxeter Arrangements
[OWP201821] (Mathematisches Forschungsinstitut Oberwolfach, 20181022)We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit ... 
On VietorisRips Complexes of Ellipses
[OWP201711] (Mathematisches Forschungsinstitut Oberwolfach, 20170425)For $X$ a metric space and $r > 0$ a scale parameter, the Vietoris–Rips complex $VR_<(X; r)$ (resp. $VR_≤(X; r)$) has $X$ as its vertex set, and a finite subset $\sigma \subseteq X$ as a simplex whenever the diameter of ... 
The PelletierRessayre Hidden Symmetry for LittlewoodRichardson Coefficients
[OWP202018] (Mathematisches Forschungsinstitut Oberwolfach, 20200908)We prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield. 
Plethysms, replicated Schur functions and series, with applications to vertex operators
[OWP201012] (Mathematisches Forschungsinstitut Oberwolfach, 20100314)Specializations of Schur functions are exploited to define and evaluate the Schur functions $s_\lambda [\alpha X]$ and plethysms $s_\lambda [\alpha s_\nu(X))]$ for any $\alpha$integer, real or complex. Plethysms are then ... 
Positive Margins and Primary Decomposition
[OWP201206] (Mathematisches Forschungsinstitut Oberwolfach, 2012)We study random walks on contingency tables with fixed marginals, corresponding to a (loglinear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that ... 
Rank Deviations for Overpartitions
[OWP202311] (Mathematisches Forschungsinstitut Oberwolfach, 20230712)We prove general fomulas for the deviations of two overpartition ranks from the average, namely \begin{equation*} \overline{D}(a, M) := \sum_{n \geq 0} \Bigl( \overline{N}(a, M, n)  \frac{\overline{p}(n)}{M} \Bigr) q^n ... 
Some Homological Properties of Borel Type Ideals
[OWP202203] (Mathematisches Forschungsinstitut Oberwolfach, 20220201)We study ideals of Borel type, including $k$Borel ideals and $t$spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated ... 
The Tutte Polynomial of Ideal Arrangements
[OWP201828] (Mathematisches Forschungsinstitut Oberwolfach, 20181221)The Tutte polynomial is originally a bivariate polynomial enumerating the colorings of a graph and of its dual graph. But it reveals more of the internal structure of the graph like its number of forests, of spanning ... 
A Uniform Model for KirillovReshetikhin Crystals I: Lifting the Parabolic Quantum Bruhat Graph
[OWP201218] (Mathematisches Forschungsinstitut Oberwolfach, 2012)We consider two lifts of the parabolic quantum Bruhat graph, one into the Bruhat order in the affine Weyl group and the other into a levelzero weight poset first considered by Littelmann. The lift into the affine Weyl ... 
The Varchenko Determinant of a Coxeter Arrangement
[OWP201733] (Mathematisches Forschungsinstitut Oberwolfach, 20171124)The Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization ...