A Refinement of a Partition Theorem of Sellers
نویسنده
چکیده
Abel’s identity a1b1+a2b2+· · ·+ambm = (b1+b2+· · ·+bm)am+(b1+· · ·+bm−1)(am−1−am)+· · ·+b1(a1−a2) is used to give a refinement of a recent theorem of Sellers.
منابع مشابه
Partitions with Parts in a Finite Set
Abstract. For a finite set A of positive integers, we study the partition function pA(n). This function enumerates the partitions of the positive integer n into parts in A. We give simple proofs of some known and unknown identities and congruences for pA(n). For n in a special residue class, pA(n) is a polynomial in n. We examine these polynomials for linear factors, and the results are applied...
متن کاملBijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao
We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2, 3, 4, 6 (mod 6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.
متن کاملBijections and Congruences for Generalizations of Partition Identities of Euler and Guy
In 1958, Richard Guy proved that the number of partitions of n into odd parts greater than one equals the number of partitions of n into distinct parts with no powers of 2 allowed, which is closely related to Euler’s famous theorem that the number of partitions of n into odd parts equals the number of partitions of n into distinct parts. We consider extensions of Guy’s result, which naturally l...
متن کاملTarski Number and Configuration Equations
The concept of configuration of groups which is defined in terms of finite partitions and finite strings of elements of the group is presented by Rosenblatt and Willis. To each set of configurations, a finite system of equations known as configuration equations, is associated. Rosenblatt and Willis proved that a discrete group G is amenable if and only if every possible instance of its configur...
متن کاملCanonical Forms and Automorphisms in the Projective Space
Let C be a sequence of multisets of subspaces of a vector space Fq . We describe a practical algorithm which computes a canonical form and the stabilizer of C under the group action of the general semilinear group. It allows us to solve canonical form problems in coding theory, i.e. we are able to compute canonical forms of linear codes, Fq-linear block codes over the alphabet Fqs and random ne...
متن کامل