Equipopularity Classes in the Separable Permutations

نویسندگان

  • Michael H. Albert
  • Cheyne Homberger
  • Jay Pantone
چکیده

When two patterns occur equally often in a set of permutations, we say that these patterns are equipopular. Using both structural and analytic tools, we classify the equipopular patterns in the set of separable permutations. In particular, we show that the number of equipopularity classes for length n patterns in the separable permutations is equal to the number of partitions of the integer n− 1.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Pattern Popularity in 132-Avoiding Permutations

The popularity of a pattern p is the total number of copies of p within all permutations of a set. We address popularity in the set of 132-avoidng permutations. Bóna showed that in this set, all other non-monotone length-3 patterns are equipopular, and proved equipopularity relations between some length-k patterns of a specific form. We prove equipopularity relations between general length-k pa...

متن کامل

Equipopularity Classes of 132-Avoiding Permutations

The popularity of a pattern p in a set of permutations is the sum of the number of copies of p in each permutation of the set. We study pattern popularity in the set of 132-avoiding permutations. Two patterns are equipopular if, for all n, they have the same popularity in the set of length-n 132-avoiding permutations. There is a well-known bijection between 132-avoiding permutations and binary ...

متن کامل

Unsplittable Classes of Separable Permutations

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

متن کامل

A bijection between permutations and floorplans, and its applications

A floorplan represents the relative relations between modules on an integrated circuit. Floorplans are commonly classified as slicing, mosaic, or general. Separable and Baxter permutations are classes of permutations that can be defined in terms of forbidden subsequences. It is known that the number of slicing floorplans equals the number of separable permutations and that the number of mosaic ...

متن کامل

The Brownian Limit of Separable Permutations

Context of our work. Describing typical properties of permutations in a given class is a question that has received quite a lot of attention in the last few years. Most of the attention is focused on permutation classes Av(τ) for τ of size 3. See for instance the very precise description of the asymptotic shape of permutations in these classes by Miner and Pak [12], or the link between large ra...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Electr. J. Comb.

دوره 22  شماره 

صفحات  -

تاریخ انتشار 2015