منابع مشابه
Signed Mahonians
A classical result of MacMahon gives a simple product formula for the generating function of major index over the symmetric group. A similar factorial-type product formula for the generating function of major index together with sign was given by Gessel and Simion. Several extensions are given in this paper, including a recurrence formula, a specialization at roots of unity and type B analogues.
متن کاملSigned Degree Sequences in Signed Bipartite Graphs
A signed bipartite graph is a bipartite graph in which each edge is assigned a positive or a negative sign. Let G(U, V ) be a signed bipartite graph with U = {u1, u2, · · · , up} and V = {v1, v2, · · · , vq} . Then signed degree of ui is sdeg(ui) = di = d + i − d − i , where 1 ≤ i ≤ p and d+i ( d − i ) is the number of positive(negative) edges incident with ui , and signed degree of vj is sdeg(...
متن کاملSigned Involutions Avoiding 2-letter Signed Patterns
Let In be the class of all signed involutions in the hyperoctahedral group Bn and let In(T ) be the set of involutions in In which avoid a set T of signed patterns. In this paper, we complete a further case of the program initiated by Simion and Schmidt [6] by enumerating In(T ) for all signed permutations T ⊆ B2.
متن کاملSigned degree sequences in signed multipartite graphs
A signed k-partite graph (signed multipartite graph) is a k-partite graph in which each edge is assigned a positive or a negative sign. If G(V1, V2, · · · , Vk) is a signed k-partite graph with Vi = {vi1, vi2, · · · , vini}, 1 ≤ i ≤ k, the signed degree of vij is sdeg(vij) = dij = d + ij − d − ij , where 1 ≤ i ≤ k, 1 ≤ j ≤ ni and d + ij(d − ij) is the number of positive (negative) edges inciden...
متن کاملSigned degree sets in signed bipartite graphs
A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident with x less the number of negative edges incident with x. The set S of distinct signed degrees of the vertices of G(U, V) is called its signed degree set. In this paper, we prove that every set of ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.07.006