Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Asinowski, Andrei"'
A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs, polytopes
Externí odkaz:
http://arxiv.org/abs/2402.01483
Autor:
Asinowski, Andrei, Banderier, Cyril
We enumerate several classes of pattern-avoiding rectangulations. We establish new bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and M\"utze. We also
Externí odkaz:
http://arxiv.org/abs/2401.05558
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 24, no. 1, Combinatorics (May 24, 2022) dmtcs:7163
The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck paths consisting of steps $\{(1, k), (1, -1)\}$ such that the path stays (weakly) above the line $y=-t$, is studied. Results are proved bijectively and b
Externí odkaz:
http://arxiv.org/abs/2007.15562
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 22 no. 2, Permutation Patterns 2019, Special issues (April 30, 2021) dmtcs:6196
Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structu
Externí odkaz:
http://arxiv.org/abs/2003.04912
Publikováno v:
Europ. J. Combin. 62 (2017), 92-114
We compute the number of triangulations of a convex $k$-gon each of whose sides is subdivided by $r-1$ points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as $k$ and/or $r$ tend to in
Externí odkaz:
http://arxiv.org/abs/1604.02870
Autor:
Asinowski, Andrei
It is well-known that the number of non-crossing perfect matchings of $2k$ points in convex position in the plane is $C_k$, the $k$th Catalan number. Garc\'ia, Noy, and Tejel proved in 2000 that for any set of $2k$ points in general position, the num
Externí odkaz:
http://arxiv.org/abs/1502.05332
Autor:
Asinowski, Andrei, Rote, Günter
Publikováno v:
Computational Geometry, Theory and Applications 68 (2018), 7-33
The maximum number of non-crossing straight-line perfect matchings that a set of $n$ points in the plane can have is known to be $O(10.0438^n)$ and $\Omega^*(3^n)$. The lower bound, due to Garc\'ia, Noy, and Tejel (2000) is attained by the double cha
Externí odkaz:
http://arxiv.org/abs/1502.04925
Let $X_{2k}$ be a set of $2k$ labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of $X_{2k}$. Two such matchings, $M$ and $M'$, are disjoint compatible if they do not have common edg
Externí odkaz:
http://arxiv.org/abs/1403.5546
Let $A,B$ with $|A| = m$ and $|B| = n\ge m$ be two sets. We assume that every element $a\in A$ has a reference list over all elements from $B$. We call an injective mapping $\tau$ from $A$ to $B$ a matching. A blocking coalition of $\tau$ is a subset
Externí odkaz:
http://arxiv.org/abs/1401.5354
Autor:
Asinowski, Andrei1,2 (AUTHOR), Barequet, Gill3 (AUTHOR) barequet@cs.technion.ac.il, Zheng, Yufei3,4 (AUTHOR)
Publikováno v:
Annals of Combinatorics. Dec2022, Vol. 26 Issue 4, p997-1020. 24p.