balls Bell numbers binary word binomial Cayley table chromatic polynomial closed formula codeword coefﬁcient color patterns column combinatorial Compute Conﬁrm Corollary corresponding cube cycle index cycle index polynomial cycle type deﬁned Deﬁnition degree sequence Denote dictionary order disjoint cycle factorization edges elementary symmetric functions elements Equation equivalent exactly Example Exercise exponential generating function Figure ﬁnd ﬁrst ﬁxed but arbitrary ﬁxed points follows G Ľ G Sm graph G group of degree Hadamard matrix Hint identity illustrated in Fig incidence matrix inequivalent integer isomorphic Lemma Let G linear code minimal symmetric polynomials modulo monomial multinomial multinomial theorem multiple nonisomorphic graphs nonnegative integer number of partitions obtained one-to-one Pascal’s permutation group plane graph positive integer Prove rearranging recurrence Section Show squares of order Stirling numbers subgraph subgroup subsets Suppose symmetric polynomials threshold graph unique urns vertex vertices yields
Page xii - It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general the more difficult) the idea. Thus the idea of an "irrational" is deeper than that of an integer; and Pythagoras's theorem is, for that reason, deeper than Euclid's.
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Russell Merris - 2000 - Turk J Math
Shujun Li - 2005 - Arxiv preprint math.NT/0509350
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John Gough - 2003 - Arxiv preprint quant-ph/0311161
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