{"id":41032,"date":"2024-09-25T11:28:02","date_gmt":"2024-09-25T11:28:02","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ad%d8%af%d8%b3-%d8%a7%d8%b3%d9%86%d9%88%db%8c%d9%84%db%8c-%d8%af%d8%b1-%d9%85%d9%88%d8%b1%d8%af-mathcal\/"},"modified":"2024-09-25T11:29:25","modified_gmt":"2024-09-25T11:29:25","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ad%d8%af%d8%b3-%d8%a7%d8%b3%d9%86%d9%88%db%8c%d9%84%db%8c-%d8%af%d8%b1-%d9%85%d9%88%d8%b1%d8%af-mathcal","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ad%d8%af%d8%b3-%d8%a7%d8%b3%d9%86%d9%88%db%8c%d9%84%db%8c-%d8%af%d8%b1-%d9%85%d9%88%d8%b1%d8%af-mathcal\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062d\u062f\u0633 \u0627\u0633\u0646\u0648\u06cc\u0644\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f mathcal{L}-\u062a\u0642\u0627\u0637\u0639 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0647\u0627 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u0648 \u0622\u0646\u0627\u0644\u0648\u06af \u0622\u0646 \u062f\u0631 \u0641\u0636\u0627\u0647\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nSnevily’s Conjecture about $\\mathcal{L}$-intersecting Families on Set Systems and its Analogue on Vector Spaces<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062d\u062f\u0633 \u0627\u0633\u0646\u0648\u06cc\u0644\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f mathcal{L}-\u062a\u0642\u0627\u0637\u0639 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0647\u0627 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u0648 \u0622\u0646\u0627\u0644\u0648\u06af \u0622\u0646 \u062f\u0631 \u0641\u0636\u0627\u0647\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nJiuqiang Liu, Guihai Yu, Lihua Feng, Yongjiang Wu<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n19<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nCombinatorics,\u062a\u0631\u06a9\u06cc\u0628\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 6 March, 2024; originally announced March 2024. , Comments: arXiv admin note: text overlap with arXiv:1701.00585 by other authors<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 6 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: Arxiv Admin \u062a\u0648\u062c\u0647: \u0645\u062a\u0646 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0628\u0627 Arxiv: 1701.00585 \u062a\u0648\u0633\u0637 \u0633\u0627\u06cc\u0631 \u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

The classical Erd\u0151s-Ko-Rado theorem on the size of an intersecting family of $k$-subsets of the set $[n] = \\{1, 2, \\dots, n\\}$ is one of the fundamental intersection theorems for set systems. After the establishment of the EKR theorem, many intersection theorems on set systems have appeared in the literature, such as the well-known Frankl-Wilson theorem, Alon-Babai-Suzuki theorem, and Grolmusz-Sudakov theorem. In 1995, Snevily proposed the conjecture that the upper bound for the size of an $\\mathcal{L}$-intersecting family of subsets of $[n]$ is ${{n} \\choose {s}}$ under the condition $\\max \\{l_{i}\\} < \\min \\{k_{j}\\}$, where $\\mathcal{L} = \\{l_{1}, \\dots, l_{s}\\}$ with $0 \\leq l_{1} < \\cdots < l_{s}$ and $k_{j}$ are subset sizes in the family. In this paper, we prove that Snevily's conjecture holds for $n \\geq {k^{2} \\choose {l_{1}+1}}s + l_{1}$, where $k$ is the maximum subset size in the family. We then derive an analogous result for $\\mathcal{L}$-intersecting families of subspaces of an $n$-dimensional vector space over a finite field $\\mathbb{F}_{q}$.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0642\u0636\u06cc\u0647 \u06a9\u0644\u0627\u0633\u06cc\u06a9 erd\u0151s-ko-rado \u062f\u0631 \u0645\u0648\u0631\u062f \u0627\u0646\u062f\u0627\u0632\u0647 \u06cc\u06a9 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0645\u062a\u0642\u0627\u0637\u0639 $ k $ -subsets \u0645\u062c\u0645\u0648\u0639\u0647 $ [n] = \\ {1 \u060c 2 \u060c \\ dots \u060c n \\} $ \u06cc\u06a9\u06cc \u0627\u0632 \u0642\u0636\u06cc\u0647 \u0647\u0627\u06cc \u0627\u0633\u0627\u0633\u06cc \u062a\u0642\u0627\u0637\u0639 \u0627\u0633\u062a\u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u062a\u0646\u0638\u06cc\u0645 \u0634\u062f\u0647.\u067e\u0633 \u0627\u0632 \u062a\u0623\u0633\u06cc\u0633 \u0642\u0636\u06cc\u0647 EKR \u060c \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0642\u0636\u06cc\u0647 \u0647\u0627\u06cc \u062a\u0642\u0627\u0637\u0639 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631 \u0627\u062f\u0628\u06cc\u0627\u062a \u0638\u0627\u0647\u0631 \u0634\u062f\u0647 \u0627\u0646\u062f \u060c \u0645\u0627\u0646\u0646\u062f \u0642\u0636\u06cc\u0647 \u0645\u0634\u0647\u0648\u0631 \u0641\u0631\u0627\u0646\u06a9\u0644-\u0648\u06cc\u0644\u0633\u0648\u0646 \u060c \u0642\u0636\u06cc\u0647 Alon-Babai-Suzuki \u0648 \u0642\u0636\u06cc\u0647 Grolmusz-Sudakov.\u062f\u0631 \u0633\u0627\u0644 1995 \u060c Snevily \u0627\u06cc\u0646 \u062d\u062f\u0633 \u0631\u0627 \u0645\u0637\u0631\u062d \u0643\u0631\u062f \u0643\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u0628\u0627\u0644\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 $ \\ Mathcal {L} $-\u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0645\u062a\u0642\u0627\u0637\u0639 \u0632\u06cc\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u0647\u0627\u06cc $ [n] $ $ {n} \\ \u0627\u0646\u062a\u062e\u0627\u0628 {s}}} $ \u062a\u062d\u062a \u0634\u0631\u0627\u06cc\u0637$ \\ max \\ {l_ {i} \\} <\\ min \\ {k_ {j} \\} $ \u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 $ \\ mathcal {l} = \\ {l_ {1} \u060c \\ \u0646\u0642\u0627\u0637 \u060c l_ {s} \\} $ \u0628\u0627$ 0 \\ leq l_ {1} <\\ cdots \n","protected":false},"excerpt":{"rendered":"

\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Snevily’s Conjecture about $\\mathcal{L}$-intersecting Families on Set Systems and its Analogue on Vector Spaces \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"closed","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[15,21],"product_tag":[639,640],"class_list":{"0":"post-41032","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-15","7":"product_cat-21","8":"product_tag-combinatorics","9":"product_tag-640","10":"pmpro-has-access","11":"desktop-align-left","12":"tablet-align-left","13":"mobile-align-left","15":"first","16":"instock","17":"downloadable","18":"shipping-taxable","19":"purchasable","20":"product-type-simple"},"yoast_head":"\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062d\u062f\u0633 \u0627\u0633\u0646\u0648\u06cc\u0644\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f mathcal{L}-\u062a\u0642\u0627\u0637\u0639 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0647\u0627 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u0648 \u0622\u0646\u0627\u0644\u0648\u06af \u0622\u0646 \u062f\u0631 \u0641\u0636\u0627\u0647\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc - 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