An involution on lattice paths between two boundaries
نویسنده
چکیده
We give an involution on the set of lattice paths from (0, 0) to (a, b) with steps N = (0, 1) and E = (1, 0) that lie between two boundaries T and B, which proves that the statistics ‘number of E steps shared with T ’ and ‘number of E steps shared with B’ have a symmetric joint distribution on this set. This generalizes a result of Deutsch for the case of Dyck paths.
منابع مشابه
Two-boundary lattice paths and parking functions
We describe an involution on a set of sequences associated with lattice paths with north or east steps constrained to lie between two arbitrary boundaries. This involution yields recursions (from which determinantal formulas can be derived) for the number and area enumerator of such paths. An analogous involution can be defined for parking functions with arbitrary lower and upper bounds. From t...
متن کاملBijections for lattice paths between two boundaries
We prove that on the set of lattice paths with steps N = (0, 1) and E = (1, 0) that lie between two boundaries B and T , the two statistics ‘number of E steps shared with B’ and ‘number of E steps shared with T ’ have a symmetric joint distribution. We give an involution that switches these statistics, preserves additional parameters, and generalizes to paths that contain steps S = (0,−1) at pr...
متن کاملList of Publications with Abstracts
We prove that on the set of lattice paths with steps N = (0, 1) and E = (1, 0) that lie between two fixed boundaries T and B (which are themselves lattice paths), the statistics ‘number of E steps shared with B’ and ‘number of E steps shared with T ’ have a symmetric joint distribution. To do so, we give an involution that switches these statistics, preserves additional parameters, and generali...
متن کاملBijections from Dyck paths to 321-avoiding permutations revisited
There are at least three di erent bijections in the literature from Dyck paths to 321-avoiding permutations, due to Billey-Jockusch-Stanley, Krattenthaler, and Mansour-Deng-Du. How di erent are they? Denoting them B;K;M respectively, we show that M = B Æ L = K Æ L where L is the classical Kreweras-Lalanne involution on Dyck paths and L0, also an involution, is a sort of derivative of L. Thus K ...
متن کاملA Simplified Curved Boundary Condition in Stationary/Moving Boundaries for the Lattice Boltzmann Method
Lattice Boltzmann method is one of computational fluid dynamic subdivisions. Despite complicated mathematics involved in its background, end simple relations dominate on it; so in comparison to the conventional computational fluid dynamic methods, simpler computer programs are needed. Due to its characteristics for parallel programming, this method is considered efficient for the simulation of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011