Partition Identities I: Sandwich Theorems and Logical 0-1 Laws

نویسندگان

  • Jason P. Bell
  • Stanley Burris
چکیده

The Sandwich Theorems proved in this paper give a new method to show that the partition function a(n) of a partition identity

برای دانلود رایگان 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

New Weighted Rogers-ramanujan Partition Theorems and Their Implications

This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi’s celebrated triple product identity for theta functions, Sylvester’s famous refinement of Euler’s theorem, as we...

متن کامل

Lecture hall sequences, q-series, and asymmetric partition identities

We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that they involve partitions into parts from asymmetric residue classes, much like the little Göllnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Göllnitz theorems. Finally,...

متن کامل

New Combinatorial Interpretations of Two Analytic Identities

Two generalized partition theorems involving partitions with " n + 1 copies of n " and " n + 2 copies of n ", respectively, are proved. These theorems have potential of yielding infinite Rogers-Ramanujan type identities on MacMahon's lines. Five particular cases are also discussed. Among them three are known and two provide new combinatorial interpretations of two known ^-identities.

متن کامل

New Interpretations of Two Analytic Identities 563 2

Two generalized partition theorems involving partitions with " n + 1 copies of n " and " n + 2 copies of n ", respectively, are proved. These theorems have potential of yielding infinite Rogers-Ramanujan type identities on MacMahon's lines. Five particular cases are also discussed. Among them three are known and two provide new combinatorial interpretations of two known ^-identities.

متن کامل

Limit Laws for Random Exponentials

We study the limiting distribution of the sum SN (t) = ∑N i=1 e tXi as t→∞, N →∞, where (Xi) are i.i.d. random variables. Attention to such exponential sums has been motivated by various problems in the theory of random media. Examples include the quenched mean population size of branching random processes with random branching rates and the partition function of Derrida’s Random Energy Model. ...

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

عنوان ژورنال:
  • Electr. J. Comb.

دوره 11  شماره 

صفحات  -

تاریخ انتشار 2004