DEVELOPMENTS OF A PFAFFIAN
نویسندگان
چکیده
منابع مشابه
A Pfaffian-Hafnian Analogue of Borchardt's Identity
We prove Pf ( xi − xj (xi + xj) ) 1≤i,j≤2n = ∏ 1≤i<j≤2n xi − xj xi + xj · Hf ( 1 xi + xj ) 1≤i,j≤2n (and its variants) by using complex analysis. This identity can be regarded as a Pfaffian–Hafnian analogue of Borchardt’s identity and as a generalization of Schur’s identity.
متن کاملGenerating the Pfaffian closure with total Pfaffian functions
Given an o-minimal expansion R of the real field, we show that the structure obtained from R by iterating the operation of adding all total Pfaffian functions over R defines the same sets as the Pfaffian closure of R . 2010 Mathematics Subject Classification 14P10,03C64 (primary); 58A17 (secondary)
متن کاملα-Pfaffian, pfaffian point process and shifted Schur measure
For any complex number α and any even-size skew-symmetric matrix B, we define a generalization pf α (B) of the pfaffian pf(B) which we call the α-pfaffian. The α-pfaffian is a pfaffian analogue of the α-determinant studied in [ST] and [V]. It gives the pfaffian at α = −1. We give some formulas for α-pfaffians and study the positivity. Further we define point processes determined by the α-pfaffi...
متن کاملTowards a Characterisation of Pfaffian graphs
A bipartite graph G is known to be Pfaffian if and only if it does not contain an even subdivision H of K3,3 such that G − V H contains a 1-factor. However a general characterisation of Pfaffian graphs in terms of forbidden subgraphs is currently not known. In this paper we describe a possible approach to the derivation of such a characterisation. We also extend the characterisation for biparti...
متن کاملA Characterisation of Pfaffian Near Bipartite Graphs
A graph is 1-extendible if every edge has a 1-factor containing it. A 1-extendible non-bipartite graph G is said to be near bipartite if there exist edges e1 and e2 such that G − {e1, e2} is 1-extendible and bipartite. We characterise the Pfaffian near bipartite graphs in terms of forbidden subgraphs. The theorem extends an earlier characterisation of Pfaffian bipartite graphs.
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ژورنال
عنوان ژورنال: Transactions of the South African Philosophical Society
سال: 1904
ISSN: 2156-0382
DOI: 10.1080/21560382.1904.9626430