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the number of graph homomorphisms between paths and cycles with loops, a problem from stanley’s enumerative combinatorics
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نویسنده
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bandpey zeinab ,farley jonathan
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منبع
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transactions on combinatorics - 2023 - دوره : 12 - شماره : 3 - صفحه:115 -130
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چکیده
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Abstract. let gk(n) denote the number of sequences t1, . . . , tn in {0, 1, . . . , k − 1} such that tj+1 ≡ tj − 1, tj or tj + 1 (mod k), 1 ≤ j ≤ n, (where tn+1 is identified with t1). it is proved combinatorially that g4(n) = 3n + 2 + (−1)n and g6(n) = 3n + 2n+1 + (−1)n. this solves a problem from richard p. stanley’s 1986 text, enumerative combinatorics.
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کلیدواژه
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trinomial coefficient ,path ,cycle ,(graph) homomorphism ,transfer matrix method
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آدرس
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college drive, northern virginia community college, department of mathematics, usa, college drive, northern virginia community college, department of mathematics, usa
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پست الکترونیکی
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jonathan.farley@morgan.edu
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Authors
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