منابع مشابه
A Pentagonal Number Sieve
We prove a general pentagonal sieve theorem that has corollaries such as the following First the number of pairs of partitions of n that have no parts in common is p n p n p n p n p n Second if two unlabeled rooted forests of the same number of vertices are chosen i u a r then the probability that they have no common tree is Third if f g are two monic polynomials of the same degree over the eld...
متن کاملOn Wachspress pentagonal patches
Wachspress quadrilateral patches have been recently studied from the point of view of applications to surface modelling in CAGD [1], [3], [4]. Some more applications for defining barycentric coordinates for arbitrary polygons have also been presented in [5] [9]. The purpose of the present paper is to introduce non-negative Wachspress rational basis functions for surface modelling on pentagonal ...
متن کاملThe truncated pentagonal number theorem
A new expansion is given for partial sums of Euler’s pentagonal number series. As a corollary we derive an infinite family of inequalities for the partition function, p(n).
متن کاملTuring patterns with pentagonal symmetry.
We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of disk sizes, offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids. Using this pattern as a seed, more complex biological structures can b...
متن کاملAn integration of Euler's pentagonal partition
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler’s recurrence based on the pentagonal numbers, but where the coefficients result from a discrete integration of Euler’s coefficients. Both a bijective proof and one based on generating functions show the equivalence of the subjec...
متن کاملذخیره 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: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8624