Zobrazeno 1 - 10
of 2 775
pro vyhledávání: '"A. Prodinger"'
Autor:
Prodinger, Helmut
Descents of odd length in Dyck paths are discussed, taking care of some variations. The approach is based on generating functions and the kernel method and augments relations about them from the Encyclopedia of Integer Sequences, that were pointed ou
Externí odkaz:
http://arxiv.org/abs/2408.01290
Autor:
Prodinger, Helmut
Instead of $k$-Dyck paths we consider the equivalent concept of $k$-non-crossing trees. This is our preferred approach relative to down-step statistics modulo $k$ (first studied by Heuberger, Selkirk, and Wagner by different methods). One symmetry ar
Externí odkaz:
http://arxiv.org/abs/2403.13937
Autor:
Prodinger, Helmut
Dispersed Dyck paths are Dyck paths, with possible flat steps on level 0. We revisit and augment questions about them from the Encyclopedia of Integer Sequences, in a systematic way that uses generating functions and the kernel method.
Externí odkaz:
http://arxiv.org/abs/2402.13026
Autor:
Prodinger, Helmut
Stanley considered Dyck paths where each maximal run of down-steps to the $x$-axis has odd length; they are also enumerated by (shifted) Catalan numbers. Prefixes of these combinatorial objects are enumerated using the kernel method. A more challengi
Externí odkaz:
http://arxiv.org/abs/2402.01429
Autor:
Prodinger, Helmut
Carlitz-compositions follow the restrictions of neighbouring parts $\sigma_{i-1}\neq\sigma_{i}$. The recently introduced Arndt-compositions have to satisfy $\sigma_{2i-1}>\sigma_{2i}$. The two concepts are combined to new and exciting objects that we
Externí odkaz:
http://arxiv.org/abs/2312.05081
Autor:
Prodinger, Helmut
Motzkin excursions and meanders are revisited. This is considered in the context of forbidden patterns. Previous work by Asinowski, Banderier, Gittenberger, and Roitner is continued. Motzkin paths of bounded height are considered, leading to matrix e
Externí odkaz:
http://arxiv.org/abs/2310.12497
Autor:
Prodinger, Helmut
A well-known bijection between Motzkin paths and ordered trees with outdegree always $\le2$, is lifted to Grand Motzkin paths (the nonnegativity is dropped) and an ordered list of an odd number of such $\{0,1,2\}$ trees. This offers an alternative to
Externí odkaz:
http://arxiv.org/abs/2308.07884
Autor:
Prodinger, Helmut
There was recent interest in Motzkin paths without peaks (peak: up-step followed immediately by down-step); additional results about this interesting family is worked out. The new results are the enumeration of such paths that live in a strip $[0..\e
Externí odkaz:
http://arxiv.org/abs/2308.03080
Autor:
Prahlad K. Routh, Evgeniy Redekop, Sebastian Prodinger, Jessi E. S. van der Hoeven, Kang Rui Garrick Lim, Joanna Aizenberg, Maarten Nachtegaal, Adam H. Clark, Anatoly I. Frenkel
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-10 (2024)
Abstract Restructuring of metal components on bimetallic nanoparticle surfaces in response to the changes in reactive environment is a ubiquitous phenomenon whose potential for the design of tunable catalysts is underexplored. The main challenge is t
Externí odkaz:
https://doaj.org/article/50e8c2272e8e479da153d54041ccb718
Autor:
Prodinger, Helmut
So called $S$-Motzkin paths are combined the concepts `catastrophes' and `air pockets. The enumeration is done by properly set up bivariate generating functions which can be extended using the kernel method.
Comment: Very early version of the ma
Comment: Very early version of the ma
Externí odkaz:
http://arxiv.org/abs/2302.07233