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most citedThe LOFAR Two-metre Sky Survey -- V. Second data release

489 citations

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18 papers · 1 filter

math.CO2024★ 2 cited

Recurrence and transience for non-Archimedean and directed graphs

Matthias Keller, Anna Muranova

We introduce the notion of recurrence and transience for graphs over non-Archimedean ordered field. To do so we relate these graphs to random walks of directed graphs over the real…

math.CO2020★ 7 cited

On the Grassmann Graph of Linear Codes

Ilaria Cardinali, Luca Giuzzi, Mariusz Kwiatkowski

Let be the Grassmann graph formed by the -dimensional subspaces of a vector space of dimension over a field and, for , l…

math.CO2020

The effective impedances of infinite ladder networks and Dirichlet problem on graphs

Anna Muranova

We calculate effective impedances of infinite - and - ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves…

math.CO2018

Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules

Metod Saniga, Edyta Bartnicka

It is shown that there exists a particular associative ring with unity of order 16 such that the relations between nonunimodular free cyclic submodules of its two-dimensional free…

math.CO2018★ 1 cited

On two types of -monodromy in triangulations of surfaces

Mark Pankov, Adam Tyc

Let be a triangulation of a connected closed -dimensional (not necessarily orientable) surface. Using zigzags (closed left-right paths), for every face of we define the…

math.CO2017

Connected sums of -knotted triangulations

Mark Pankov, Adam Tyc

An embedded graph is called -knotted if it contains the unique zigzag (up to reversing). We consider -knotted triangulations, i.e. -knotted embedded graphs whose faces are…

math.CO2017

Apartments preserving transformations of Grassmannians of infinite-dimensional vector spaces

Mark Pankov

We define the Grassmannians of an infinite-dimensional vector space as the orbits of the action of the general linear group on the set of all subspaces. Let ${\ma…

math.CO2016★ 4 cited

Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables

Adam Doliwa

We introduce a coloured generalization of the Hopf algebra of non-commutative symmetric functions described as a subalgebra of the of rooted ordered coloured tree…

math.CO2015

Orthogonal apartments in Hilbert Grassmannians

Mark Pankov

Let be an infinite-dimensional complex Hilbert space and let be the logic formed by all closed subspaces of . For every natural we denote by ${\mathcal…

math.CO2015

On the distance between linear codes

Mariusz Kwiatkowski, Mark Pankov

Let be an -dimensional vector space over the finite field consisting of elements and let be the Grassmann graph formed by -dimensional subspaces of , $1…

math.CO2015★ 1 cited

Isometric embeddings of polar Grassmannians and metric characterizations of their apartments

Mariusz Kwiatkowski, Mark Pankov

We describe isometric embeddings of polar Grassmann graphs formed by non-maximal singular subspaces. In almost all cases, they are induced by collinearity preserving injections of…

math.CO2015★ 4 cited

The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers

Andrzej Matraś, Artur Siemaszko

The distant graph of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein…

math.CO2011

Characterization of apartments in polar Grassmannians

Mark Pankov

Buildings of types and are defined by rank polar spaces. The associated building Grassmannians are polar and half-spin Grassmannians. Apartments i…

math.CO2011

Isometric embeddings of half-cube graphs in half-spin Grassmannians

Mark Pankov

Let be a polar space of type . Denote by , the associated half-spin Grassmannians and write for the corresponding hal…

math.CO2010

Metric characterization of apartments in dual polar spaces

Mark Pankov

Let be a polar space of rank and let , be the polar Grassmannian formed by -dimensional singular subspaces of . The corres…

math.CO2010

Isometric embeddings of Johnson graphs in Grassmann graphs

Mark Pankov

Let be an -dimensional vector space () and let be the Grassmannian formed by all -dimensional subspaces of . The corresponding Gr…

math.CO2006

Base subsets of polar Grassmannians

Mark Pankov

Let be a thick building of type . Let also be the Grassmannian of -dimensional singular subspaces of the assoc…

math.CO2006

Base subsets of symplectic Grassmannians

Mark Pankov

Let and be -dimensional vector spaces over fields and . Let also and be non-degenerate symplectic forms. Denote by…