Basic analytic combinatorics of directed lattice paths

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Basic analytic combinatorics of directed lattice paths

This paper develops a uni(ed enumerative and asymptotic theory of directed two-dimensional lattice paths in half-planes and quarter-planes. The lattice paths are speci(ed by a (nite set of rules that are both time and space homogeneous, and have a privileged direction of increase. (They are then essentially one-dimensional objects.) The theory relies on a speci(c “kernel method” that provides a...

متن کامل

Analytic Combinatorics of Lattice Paths: Enumeration and Asymptotics for the Average Area†

This paper tackles the enumeration and asymptotics of the area below directed lattice paths (walks on N, with a finite set of jumps). It is a nice surprise (obtained via the “kernel method”) that the generating functions of the moments of the area are algebraic functions, expressible as symmetric functions in terms of the roots of the kernel. For a large class of walks, we give full asymptotics...

متن کامل

Analytic Combinatorics of Lattice Paths: Enumeration and Asymptotics for the Area

This paper tackles the enumeration and asymptotics of the area below directed lattice paths (walks on N, with a finite set of jumps). It is a nice surprise (obtained via the “kernel method”) that the generating functions of the moments of the area are algebraic functions, expressible as symmetric functions in terms of the roots of the kernel. For a large class of walks, we give full asymptotics...

متن کامل

The Order Steps of an Analytic Combinatorics

‎Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures‎. ‎This theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines‎, ‎including probability theory‎, ‎statistical physics‎, ‎computational biology and information theory‎. ‎With a caref...

متن کامل

Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are usefu...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 2002

ISSN: 0304-3975

DOI: 10.1016/s0304-3975(02)00007-5