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.
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Björklund and Husfeldt developed a randomized polynomial time algorithm to solve the shortest two disjoint paths problem. Their algorithm is based on computation of permanents modulo 4 and the isolation lemma. In this paper, we consider the following generalization of the shortest two disjoint paths problem, and develop a similar algebraic algorithm. The shortest perfect (A + B)-path packing pr...
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We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with nonnegative entries. We introduce a condition under which the Barvinok estimator achieves subexponential errors, and show that this condition is almost optimal. Using that hafnians count the number of perfect matchings in graphs, we conclude that Barvinok’s estimator gives a polynomialtim...
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Chen’s lemma on iterated integrals implies that certain identities involving multiple integrals, such as the de Bruijn and Wick formulas, amount to combinatorial identities for Pfaffians and hafnians in shuffle algebras. We provide direct algebraic proofs of such shuffle identities, and obtain various generalizations. We also discuss some Pfaffian identities due to Sundquist and Ishikawa-Wakaya...
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We investigate a conjecture of Haglund that asserts that certain graph polynomials have only real roots. We prove a multivariate generalization of this conjecture for the special case of threshold graphs. Résumé. Nous étudions une conjecture de Haglund qui affirme que certaines polynômes des graphes ont uniquement des racines réelles. Nous prouvons une généralisation multivariée de cette conjec...
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ژورنال
عنوان ژورنال: Microscopy and Microanalysis
سال: 2005
ISSN: 1431-9276,1435-8115
DOI: 10.1017/s1431927605510730