Titlebook: Algebraic Combinatorics; Walks, Trees, Tablea Richard P. Stanley Textbook 2018Latest edition Springer International Publishing AG, part of

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Cubes and the Radon Transform,Let us now consider a more interesting example of a graph ., one whose eigenvalues have come up in a variety of applications. Let . denote the cyclic group of order 2, with elements 0 and 1 and group operation being addition modulo 2.

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A Glimpse of Young Tableaux,We defined in Chapter . Young’s lattice .?, the poset of all partitions of all nonnegative integers, ordered by containment of their Young diagrams.

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The Matrix-Tree Theorem,The Matrix-Tree Theorem is a formula for the number of spanning trees of a graph in terms of the determinant of a certain matrix. We begin with the necessary graph-theoretical background. Let . be a finite graph, allowing multiple edges but not loops. (Loops could be allowed, but they turn out to be completely irrelevant.)

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A Glimpse of Combinatorial Commutative Algebra,In this chapter we will discuss a profound connection between commutative rings and some combinatorial properties of simplicial complexes. The deepest and most interesting results in this area require a background in algebraic topology and homological algebra beyond the scope of this book.

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Richard P. StanleyIncludes a new chapter on combinatorial commutative algebra.First text on algebraic combinatorics targeted towards undergraduates.Written by the most well-known algebraic combinatorist world-wide.Cove

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Algebraic Combinatorics978-3-319-77173-1Series ISSN 0172-6056 Series E-ISSN 2197-5604

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,Epigenetic Therapy for Alzheimer’s Disease,d elements, such as {1, 1, 3, 4, 4, 4, 6, 6}. We are only concerned with how many times each element occurs and not on any ordering of the elements. Thus for instance {2, 1, 2, 4, 1, 2} and {1, 1, 2, 2, 2, 4} are the same multiset: they each contain two 1’s, three 2’s, and one 4 (and no other elements).