منابع مشابه
Standard Young tableaux and colored Motzkin paths
In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the n-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length n. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most 2d+ 1 rows and the set of ...
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The starting point of this work is the discovery of a new and direct construction that relies bijectively the permutations of length n to some weighted Dyck paths named subdivided Laguerre histories. These objects correspond to the combinatorial interpretation of the development of the generating function for factorial numbers in terms of a Stieltjes continued fraction [9]. Such a bijection has...
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Kim and Drake used generating functions to prove that the number of 2-distant noncrossing matchings, which are in bijection with little Schröder paths, is the same as the weight of Dyck paths in which downsteps from even height have weight 2. This work presents bijections from those Dyck paths to little Schröder paths, and from a similar set of Dyck paths to big Schröder paths. We show the effe...
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The study of representations of aane Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any nite Coxeter group. This paper is completely independent of aane Hecke algebra theory and is purely combinatorial. We deene generalized shapes and standard Young tableaux and show that these new objects coincide with the classical ones for root...
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We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics. In this paper K is a field of characteristic zero and all vector spaces are over K. A K[S]-module is a collection of K[Sr]-modules of the symmetric groups Sr. A H(q)-module is a collect...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2020
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-019-00482-3