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pro vyhledávání: '"Kotlar, Daniel"'
A Young diagram $Y$ is called wide if every sub-diagram $Z$ formed by a subset of the rows of $Y$ dominates $Z'$, the conjugate of $Z$. A Young diagram $Y$ is called Latin if its squares can be assigned numbers so that for each $i$, the $i$th row is
Externí odkaz:
http://arxiv.org/abs/2311.17670
Publikováno v:
Computational and Mathematical Methods 3:3 (2021) paper e1094
Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for developing
Externí odkaz:
http://arxiv.org/abs/1910.10103
Autor:
Kotlar, Daniel, Ziv, Ran
Let $M$ and $N$ be two matroids on the same ground set. We generalize results of Drisko and Chapell by showing that any $2n-1$ sets of size $n$ in $M \cap N$ have a rainbow set of size $n$ in $M \cap N$.
Externí odkaz:
http://arxiv.org/abs/1407.7321
Given sets $F_1, \ldots ,F_n$, a {\em partial rainbow function} is a partial choice function of the sets $F_i$. A {\em partial rainbow set} is the range of a partial rainbow function. Aharoni and Berger \cite{AhBer} conjectured that if $M$ and $N$ ar
Externí odkaz:
http://arxiv.org/abs/1405.3119
Autor:
Kotlar, Daniel, Ziv, Ran
Publikováno v:
European Journal of Combinatorics. Vol. 38, 97-101 (2013)
Let $g(n)$ be the least number such that every collection of $n$ matchings, each of size at least $g(n)$, in a bipartite graph, has a full rainbow matching. Aharoni and Berger \cite{AhBer} conjectured that $g(n)=n+1$ for every $n>1$. This generalizes
Externí odkaz:
http://arxiv.org/abs/1305.1466
Autor:
Kotlar, Daniel
Publikováno v:
Discrete Mathematics. 331, 74--82 (2014)
An algorithm that uses the cycle structure of the rows, or the columns, of a Latin square to compute its autotopy group is introduced. As a result, a bound for the size of the autotopy group is obtained. This bound is used to show that the computatio
Externí odkaz:
http://arxiv.org/abs/1305.1406
Autor:
Kotlar, Daniel, Ziv, Ran
Publikováno v:
Electronic J. Combinatorics, volume 19, Issue 2 (2012)
We suggest and explore a matroidal version of the Brualdi - Ryser conjecture about Latin squares. We prove that any $n\times n$ matrix, whose rows and columns are bases of a matroid, has an independent partial transversal of length $\lceil2n/3\rceil$
Externí odkaz:
http://arxiv.org/abs/1204.5274
Autor:
Kotlar, Daniel
Publikováno v:
Electronic J. Combinatorics, volume 19(4) (2012)
Expressions involving the product of the permanent with the (n-1)th power of the determinant of a matrix of indeterminates, and of (0,1)-matrices, are shown to be related to two conjectures that extend the Alon-Tarsi Latin square conjecture to odd di
Externí odkaz:
http://arxiv.org/abs/1204.5276
Autor:
Kotlar, Daniel
Publikováno v:
Electronic J. Combinatorics, volume 19(3) (2012)
The parity type of a Latin square is defined in terms of the numbers of even and odd rows and columns. It is related to an Alon-Tarsi-like conjecture that applies to Latin squares of odd order. Parity types are used to derive upper bounds for the siz
Externí odkaz:
http://arxiv.org/abs/1203.0223
Autor:
Kotlar, Daniel
The effect of replacing a basis element on the way the basis spans other elements is studied. This leads to a new characterization of binary matroids.
Comment: The content of this manuscript in contained in 1110.5166
Comment: The content of this manuscript in contained in 1110.5166
Externí odkaz:
http://arxiv.org/abs/1112.2617