We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete Applied Math...
Emmanuel Kowalski and William Sawin proved, using a deep independence result of Kloosterman sheaves, that the polygonal paths joining the partial sums of the normalized classical Kloosterman sums S(a,b0;p)/p^{1/2} converge in the sense of finite dist...
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Jun 7, 2021 · I would like to know the full list of variables that I can use in Windows Explorer or related relative paths that is accepted by Windows 10. Variables like %appdata ...
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A graph is called (edge)-SIT if for some probability measure on paths, the number of mutual edges in two independent paths has finite mean. We show that transience is equivalent to the property of (edge)-SIT....
Dyck paths are among the most heavily studied Catalan families. This paper is a continuation of [2]. In the paper we are dealing with the numbering of Dyck paths, the terms of the OEIS sequence A036991 or Dyck numbers. We consider triplets of terms o...
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From quick tips to live sessions, Skilljar makes training dynamic with personalized paths and certifications, inspiring discovery. Monetize effortlessly with flexible pricing options for courses, paths, …
A bijection is constructed between two sets of height restricted lattice paths by means of translating them in two tree classe, namely plane trees and Elena trees. An old bijection between them can be used now for that actual problem....
An impact of integration over the paths of the Levy flights on the quantum mechanical kernel has been studied. Analytical expression for a free particle kernel has been obtained in terms of the Fox H-function. A new equation for the kernel of a par...
We show that our algorithm for inverting the sweep map on (2n, n)-Dyck paths works for any (kn, n)-Dyck path, where k is an arbitrary positive integer....
We introduce a simple, rank-based algorithm for inverting the sweep map on (2n,n)-Dyck paths....
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As observed by Rautenbach and Sereni (arXiv:1302.5503) there is a gap in the proof of the theorem of Balister et al. (Longest paths in circular arc graphs, Combin. Probab. Comput., 13, No. 3, 311-317 (2004)), which states that the intersection of all...
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We exhibit a new obstacle to the nascent algorithmic theory for classes excluding an induced minor. We indeed show that on the class of string graphs -- which avoids the 1-subdivision of, say, $K_5$ as an induced minor -- Induced 2-Disjoint Paths is...
We study the function $H_n(C_{2k})$, the maximum number of Hamilton paths such that the union of any pair of them contains $C_{2k}$ as a subgraph. We give upper bounds on this quantity for $k\ge 3$, improving results of Harcos and Soltész, and we sh...
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